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2,300 | The Mackey-Gleason Problem | math.OA | Let $A$ be a von Neumann algebra with no direct summand of Type $\roman I_2$,
and let $\scr P(A)$ be its lattice of projections. Let $X$ be a Banach space.
Let $m\:\scr P(A)\to X$ be a bounded function such that $m(p+q)=m(p)+m(q)$
whenever $p$ and $q$ are orthogonal projections. The main theorem states that
$m$ has a u... | math |
2,301 | Voiculescu theorem, Sobolev lemma, and extensions of smooth algebras | math.OA | We present the analytic foundation of a unified B-D-F extension functor
$\operatorname{Ext}_\tau$ on the category of noncommutative smooth algebras,
for any Fr\'echet operator ideal $\Cal K_\tau$. Combining the techniques
devised by Arveson and Voiculescu, we generalize Voiculescu's theorem to smooth
algebras and Fr\'e... | math |
2,302 | A splitting property for subalgebras of tensor products | math.OA | We prove a basic result about tensor products of a $\text{II}_1$ factor with
a finite von Neumann algebra and use it to answer, affirmatively, a question
asked by S. Popa about maximal injective factors. | math |
2,303 | Bourgain algebras, minimal envelopes, minimal support sets, and some applications | math.OA | We explicitly compute certain Douglas algebras that are invariant under both
the Bourgain map and the minimal envelope map. We also compute the Bourgain
algebra and the minimal envelope of the maximal subalgebras of a certain singly
generated Douglas algebra. | math |
2,304 | Relative cohomology of Banach algebras | math.OA | Let $A$ be a Banach algebra, not necessarily unital, and let $B$ be a closed
subalgebra of $A$. We establish a connection between the Banach cyclic
cohomology group $ {\cal{HC}}^n(A)$ of $A$ and the Banach $B$-relative cyclic
cohomology group $ {\cal{HC}}^n_B(A) $ of $A$. We prove that, for a Banach
algebra $A$ with a ... | math |
2,305 | Some conditions on Douglas algebras that imply the invariance of the minimal envelope map | math.OA | We give several conditions on certain families of Douglas algebras that imply
that the minimal envelope of the given algebra is the algebra itself. We also
prove that the minimal envelope of the intersection of two Douglas algebras is
the intersection of their minimal envelope. | math |
2,306 | Algebras associated with Blaschke products of type {\it G} | math.OA | Let $\Omega$ and $\Omega_{\fin}$ be the sets of all interpolating Blaschke
products of type $G$ and of finite type $G$, respectively. Let $E$ and
$E_{\fin}$ be the Douglas algebras generated by $H^\infty$ together with the
complex conjugates of elements of $\Omega$ and $\Omega_{\fin}$, respectively.
We show that the se... | math |
2,307 | Fourier-Stieltjes algebras of locally compact groupoids | math.OA | This paper gives a first step toward extending the theory of
Fourier-Stieltjes algebras from groups to groupoids. If G is a locally compact
(second countable) groupoid, we show that B(G), the linear span of the Borel
positive definite functions on G, is a Banach algebra when represented as an
algebra of completely boun... | math |
2,308 | Conjugate operators for finite maximal subdiagonal algebras | math.OA | Let $\M$ be a von Neumann algebra with a faithful normal trace $\T$, and let
$H^\infty$ be a finite, maximal, subdiagonal algebra of $\M$. Fundamental
theorems on conjugate functions for weak$^*$\!-Dirichlet algebras are shown to
be valid for non-commutative $H^\infty$. In particular the conjugation operator
is shown t... | math |
2,309 | Excision in Banach simplicial and cyclic cohomology | math.OA | We prove that, for every extension of Banach algebras $ 0 \rightarrow B
\rightarrow A \rightarrow D \rightarrow 0 $ such that $B$ has a left or right
bounded approximate identity, the existence of an associated long exact
sequence of Banach simplicial or cyclic cohomology groups is equivalent to the
existence of one fo... | math |
2,310 | Fell bundles over groupoids | math.OA | The author provides some definitions and structural results about Fell
bundles, defined as C^*-algebra bundles over topological groupoids. Such
bundles are a mutual generalization of semi-direct products of groups with
C^*-algebras and C^*-algebra bundles over topological spaces. In particular a
Morita equivalence theo... | math |
2,311 | Nonstable K-theory for Z-stable C*-algebras | math.OA | Let Z denote the simple limit of prime dimension drop algebras that has a
unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z.
Then the homotopy groups of the group U(A) of unitaries in A are stable
invariants, namely, \pi_i(U(A)) = K_{i-1}(A) for all integers i >= 0.
Furthermore, A has cancell... | math |
2,312 | C*-actions of r-discrete groupoids and inverse semigroups | math.OA | Groupoid actions on C*-bundles and inverse semigroup actions on C*-algebras
are closely related when the groupoid is r-discrete. | math |
2,313 | Sub-Riemannian metrics for quantum Heisenberg manifolds | math.OA | Every Heisenberg manifold has a natural "sub-Riemannian" metric with
interesting properties. We describe the corresponding noncommutative metric
structure for Rieffel's quantum Heisenberg manifolds. | math |
2,314 | Ideal structure and simplicity of the C*-algebras generated by Hilbert bimodules | math.OA | Pimsner introduced the C*-algebra O_X generated by a Hilbert bimodule X over
a C*-algebra A. We look for additional conditions that X should satisfy in
order to study simplicity and, more generally, the ideal structure of O_X when
X is finite projective. We introduce two conditions: `(I)-freeness' and
`(II)-freeness', ... | math |
2,315 | Central sequence subfactors and double commutant properties | math.OA | First, we construct the Jones tower and tunnel of the central sequence
subfactor arising from a hyperfinite type II_1 subfactor with finite index and
finite depth, and prove each algebra has the double commutant property in the
ultraproduct of the enveloping II_1 factor. Next, we show the equivalence
between Popa's str... | math |
2,316 | Applications of Topological *-Algebras of Unbounded Operators | math.OA | In this paper we discuss some physical applications of topological *-algebras
of unbounded operators. Our first example is a simple system of free bosons.
Then we analyze different models which are related to this one. We also discuss
the time evolution of two interacting models of matter and bosons. We show that
for a... | math |
2,317 | Projections in Rotation Algebras and Theta Functions | math.OA | For each $\alpha \in (0,1)$, $A_\alpha$ denotes the universal $C^*$-algebra
generated by two unitaries $u$ and $v$, which satisfy the commutation relation
$uv=\exp (2\pi i\alpha)vu$. We consider the order four automorphism $\sigma$ of
$A_\alpha$ defined by $\sigma (u)=v$, $\sigma (v)=u^{-1}$ and describe a method
for c... | math |
2,318 | Almost Representations and Asymptotic Representations of Discrete Groups | math.OA | We define for discrete finitely presented groups a new property related to
their asymptotic representations. Namely we say that a groups has the property
AGA if every almost representation generates an asymptotic representation. We
give examples of groups with and without this property. For our example of a
group $G$ w... | math |
2,319 | Factorization of completely bounded bilinear operators and injectivity | math.OA | We characterize injectivity of von Neumann algebras in terms of factoring
bilinear maps as products of linear maps. | math |
2,320 | Multiplicity-free representations of commutative C*-algebras and spectral properties | math.OA | Let A be a commutative unital C*-algebra and let S denote its Gelfand
spectrum. We give some necessary and sufficient conditions for a nondegenerate
representation of A to be unitarily equivalent to a multiplicative
representation on a space L^2(S, m), where m is a positive measure on the Baire
sets of S. We also compa... | math |
2,321 | Viewing AF-algebras as graph algebras | math.OA | Every AF-algebra arises as a graph algebra in the sense of Kumjian, Pask,
Raeburn, and Renault. For AF-algebras, the diagonal subalgebra defined by
Stratila and Voiculescu is consistent with Kumjian's notion of diagonal, and
the groupoid arising from a well-chosen Bratteli diagram for A coincides with
Kumjian's twist g... | math |
2,322 | The Ext class of an approximately inner automorphism, II | math.OA | Let A be a simple unital AT algebra of real rank zero and Inn(A) the group of
inner automorphisms of A. In the previous paper we have shown that the natural
map of the group of approximately inner automorphisms into Ext(K_1(A),K_0(A))
oplus Ext(K_0(A),K_1(A)) is surjective; the kernel of this map includes the
subgroup ... | math |
2,323 | Invariant Linear Manifolds for CSL-Algebras and Nest Algebras | math.OA | Every invariant linear manifold for a CSL-algebra is a closed subspace if,
and only if, each non-zero projection in the projection lattice is generated by
finitely many atoms. In the case of a nest, this condition is equivalent to the
condition that every non-zero projection in the nest has an immediate
predecessor (th... | math |
2,324 | Boundary Functions for Ideals in Analytic Limit Algebras | math.OA | We develop a theory of boundary functions for ideals in trivially analytic
subalgebras of simple AF C*-algebras with an injective 0-cocycle, a class which
includes all full nest algebras. Boundary functions are maps from the spectrum
of the diagonal of the analytic subalgebra to itself. The relation between
boundary fu... | math |
2,325 | The Toeplitz algebra of a Hilbert bimodule | math.OA | Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X.
Pimsner constructed a C*-algebra O_X which includes, for particular choices of
X, crossed products of A by Z, the Cuntz algebras O_n, and the Cuntz-Krieger
algebras O_B. Here we analyse the representations of the corresponding Toeplitz
algebr... | math |
2,326 | Representable bimodules over C*-algebras | math.OA | Given two C*-algebras A and B, abstract A-B bimodules that can be
isometrically represented as operator bimodules are characterised in terms of
their norm. Various properties of such bimodules are given. Their theory is
very similar to those of classical normed spaces. | math |
2,327 | Metrics on states from actions of compact groups | math.OA | Let a compact Lie group act ergodically on a unital $C^*$-algebra $A$. We
consider several ways of using this structure to define metrics on the state
space of $A$. These ways involve length functions, norms on the Lie algebra,
and Dirac operators. The main thrust is to verify that the corresponding metric
topologies o... | math |
2,328 | The curvature invariant of a Hilbert module over C[z_1,...,z_d] | math.OA | A notion of curvature is introduced in multivariable operator theory and an
analogue of the Gauss-Bonnet-Chern theorem is established for graded
(contractive) Hilbert modules over the complex polynomial algebra in d
variables, d=1,2,3,....
The curvature invariant, Euler characteristic, and degree are computed for
som... | math |
2,329 | Relative positions of matroid algebras | math.OA | A classification is given for (regular) positions of direct sums of two
matroid algebras (unital algebraic limits of matrix algebras) in a matroid
superalgebra, where the individual summands have index 2 in their associated
corner algebra. A similar classification is obtained for positions of direct
sums of 2-symmetric... | math |
2,330 | On the classification of nuclear C*-algebras | math.OA | The mid-seventies' works on C*-algebras of Brown-Douglas-Fillmore and Elliott
both contained uniqueness and existence results in a now standard sense. These
papers served as keystones for two separate theories -- KK-theory and the
classification program -- which for many years parted ways with only moderate
interaction... | math |
2,331 | Structure of the group of automorphisms of C$^{*}$-algebras | math.OA | We obtain a kind of structure theorem for the automorphism group ${\rm
Aut}{\cal A}$ of a unital C$^{*}$-algebra ${\cal A}$. According to it, ${\rm
Aut}{\cal A}$ can be regarded as a subgroup of the semi-direct product of
direct product group consisting of some family of projective unitary groups and
some permutation g... | math |
2,332 | Normal conditional expectations of finite index and sets of modular generators | math.OA | Normal conditional expectations E: M --> N in M of finite index on von
Neumann algebras M with discrete center are investigated to find an estimate
for the minimal number of generators of M as a Hilbert N-module. Analyzing the
case of M being finite type I with discrete center we obtain that these von
Neumann algebras ... | math |
2,333 | Compactly-aligned discrete product systems, and generalizations of O_\infty | math.OA | The universal C*-algebras of discrete product systems generalize the
Toeplitz- Cuntz algebras and the Toeplitz algebras of discrete semigroups. We
consider a semigroup P which is quasi-lattice ordered in the sense of Nica,
and, for a product system p:E\to P, we study those representations of E, called
covariant, which ... | math |
2,334 | Grothendieck group invariants for partly self-adjoint operator algebras | math.OA | Various partially ordered Grothendieck group invariants are introduced for
general operator algebras and these are used in the classification of direct
systems and direct limits of finite-dimensional complex incidence algebras with
common reduced digraph H (systems of H-algebras). In particular the dimension
distributi... | math |
2,335 | C*-equivalences of graphs | math.OA | Several relations on graphs, including primitive equivalence, explosion
equivalence and strong shift equivalence, are examined and shown to preserve
either the graph groupoid, a construction of Kumjian, Pask, Raeburn, and
Renault, or the groupoid of a pointed version of the graph. Thus these
relations preserve either t... | math |
2,336 | The Classification of Limits of 2n-cycle Algebras | math.OA | We obtain a complete classification of the locally finite algebras and the
operator algebras, given as algebraic inductive limits and Banach algebraic
inductive limits respectively, of direct systems:
A_1 contained in A_2 contained in A_3 and so on.
Here the A_k are 2n-cycle algebras, where n is at least 3 and the ... | math |
2,337 | The K-theory of Cuntz-Krieger algebras for infinite matrices | math.OA | We compute the K-theory of the Cuntz-Krieger C^*-algebras associated to
infinite matrices. | math |
2,338 | A Microstates Approach to Relative Free Entropy | math.OA | We define and study a relative free entropy quantity, analogous in its
properties to Voiculescu's relative free entropy Chi^*(...:B). Our definition
uses matricial microstates, unlike his definition, which involves
non-commutative Hilbert transform. We prove a change of variable formula and
certain maximization results... | math |
2,339 | Weight theory for C*-algebraic quantum groups | math.OA | In this paper, we collect some technical results about weights on C*-algebras
which are useful in de theory of locally compact quantum groups in the
C*-algebra framework. We discuss the extension of a lower semi-continuous
weight to a normal weight following S. Baaj, look into slice weights and their
KSGNS-construction... | math |
2,340 | Cohomology of topological graphs and Cuntz-Pimsner algebras | math.OA | We compute the sheaf cohomology of a groupoid built from a local
homeomorphism of a locally compact space $X$. In particular, we identify the
twists over this groupoid, and its Brauer group. Our calculations refine those
made by Kumjian, Muhly, Renault and Williams in the case $X$ is the path space
of a graph, and the ... | math |
2,341 | Skew products and crossed products by coactions | math.OA | Given a labeling c of the edges of a directed graph E by elements of a
discrete group G, one can form a skew-product graph E cross_c G. We show, using
the universal properties of the various constructions involved, that there is a
coaction delta of G on C*(E) such that C*(E cross_c G) is isomorphic to the
crossed produ... | math |
2,342 | Locally compact quantum groups in the universal setting | math.OA | In this paper we associate to every reduced C*-algebraic quantum group A a
universal C*-algebraic quantum group. We fine tune a proof of Kirchberg to show
that every *-representation of a modified L1-space is generated by a unitary
corepresentation. By taking the universal enveloping C*-algebra of a dense sub
*-algebra... | math |
2,343 | On representations of partial ^*-algebras based on B-weights | math.OA | A generalization of the GNS-representation is investigated that represents
partial ^*-algebras as systems of operators acting on a partial inner product
space (PIP-space). It is based on possibly indefinite B-weights which are
closely related to the positive B-weights introduced by J.-P. Antoine, Y.
Soulet and C. Trapa... | math |
2,344 | A Note on the Representation Theory of Fell Bundles | math.OA | We show that every Fell bundle B over a locally compact group G is "proper"
in a sense recently introduced by Ng. Combining our results with those of Ng we
show that if B satisfies the "approximation property" then it is amenable in
the sense that the full and reduced cross-sectional C*-algebras coincide. | math |
2,345 | Morita-Rieffel Equivalence and Spectral Theory for Integrable Automorphism Groups of C*-Algebras | math.OA | Given a C*-dynamical system (A,G,\alpha), we discuss conditions under which
subalgebras of the multiplier algebra M(A) consisting of fixed points for
\alpha are Morita-Rieffel equivalent to ideals in the crossed product of A by
G. In case G is abelian we also develop a spectral theory, giving a necessary
and sufficient... | math |
2,346 | Discrete product systems of Hilbert bimodules | math.OA | A Hilbert bimodule is a right Hilbert module X over a C*-algebra A together
with a left action of A as adjointable operators on X. We consider families X =
{X_s :s\in P} of Hilbert bimodules, indexed by a semigroup P, which are endowed
with a multiplication which implements isomorphisms X_s\otimes_A X_t \to
X_{st}; suc... | math |
2,347 | Discrete product systems of finite-dimensional Hilbert spaces, and generalized Cuntz algebras | math.OA | To each discrete product system E of finite-dimensional Hilbert spaces we
associate a C*-algebra O_E. When E is the n-dimensional product system over N,
O_E is the Cuntz algebra O_n, and the irrational rotation algebras appear as
O_E for certain one-dimensional product systems over N^2. We give conditions
which ensure ... | math |
2,348 | Trace acaling automorphisms of certain stable AF algebras II | math.OA | Two automorphisms of a simple stable AF algebra with a finite dimensional
lattice of lower semicontinuous traces are shown to be outer conjugate if they
act in the same way on the K-group and the extremal traces are scaled by
numbers which are not equal to 1 and satisfy a certain condition (which always
holds if all th... | math |
2,349 | On certain extension properties for the space of compact operators | math.OA | Let $Z$ be a fixed separable operator space, $X\subset Y$ general separable
operator spaces, and $T:X\to Z$ a completely bounded map. $Z$ is said to have
the Complete Separable Extension Property (CSEP) if every such map admits a
completely bounded extension to $Y$; the Mixed Separable Extension Property
(MSEP) if ever... | math |
2,350 | Nest Representations of TAF Algebras | math.OA | A nest representation of a strongly maximal TAF algebra $A$ is a
representation $\pi$ for which $\operatorname{Lat} \pi(A) is totally ordered.
We prove that if the spectrum of $A$ is totally ordered, or if
$\operatorname{Lat} \pi(A)$ contains an atom, then $\operatorname{ker} \pi$ is
a meet irreducible ideal. | math |
2,351 | Cuntz-like algebras | math.OA | The usual crossed product construction which associates to the homeomorphism
$T$ of the locally compact space $X$ the C$^*$-algebra $C^*(X,T)$ is extended
to the case of a partial local homeomorphism $T$. For example, the
Cuntz-Krieger algebras are the C$^*$-algebras of the one-sided Markov shifts.
The generalizations ... | math |
2,352 | Stable laws and domains of attraction in free probability theory | math.OA | In this paper we determine the distributional behavior of sums of free (in
the sense of Voiculescu) identically distributed, infinitesimal random
variables. The theory is shown to parallel the classical theory of independent
random variables, though the limit laws are usually quite different. Our work
subsumes all prev... | math |
2,353 | Amenability of Hopf C^*-algebras | math.OA | Three natural definitions for amenability of general Hopf C^*-algebras (all
of them being generalizations of the case of locally compact groups) were given
and the relations between them were studied. Moreover, amenability in the
situation of duality of Hopf C^*-algebras was also studied. | math |
2,354 | Approximation property of $C^*$-algebraic Bundles | math.OA | In this paper, we will define the reduced cross-sectional $C^*$-algebras of
$C^*$-algebraic bundles over locally compact groups and show that if a
$C^*$-algebraic bundle has the approximation property (defined similarly as in
the discrete case), then the full cross-sectional $C^*$-algebra and the reduced
one coincide. ... | math |
2,355 | Stable Ranks, K-Groups and Witt Groups of some Banach and C-star Algebras | math.OA | We show that certain dense and spectral invariant subalgebras of a
$C^*$-algebra have the same bilateral Bass stable rank. This is a partial
answer for (a version of) an open problem raised by R.G. Swan. Then, for
certain Banach algebras, we indicate when the homotopy groups
$\pi_{i}(GL_{n}(A))$ stabilize for large $n$... | math |
2,356 | Modules over operator algebras, and the maximal C^*-dilation | math.OA | We continue our study of the general theory of possibly nonselfadjoint
algebras of operators on a Hilbert space, and modules over such algebras,
developing a little more technology to connect `nonselfadjoint operator
algebra' with the C$^*-$algebraic framework. More particularly, we make use of
the universal, or maxima... | math |
2,357 | Regular Operators on Hilbert C^*-modules | math.OA | A regular operator T on a Hilbert C^*-module is defined just like a closed
operator on a Hilbert space, with the extra condition that the range of
(I+T^*T) is dense. Semiregular operators are a slightly larger class of
operators that may not have this property. It is shown that, like in the case
of regular operators, o... | math |
2,358 | Extremal richness of multiplier and corona algebras of simple C*-algebras with real rank zero | math.OA | In this paper we investigate the extremal richness of the multiplier algebra
$M(A)$ and the corona algebra $M(A)/A$, for a simple C*-algebra $A$ with real
rank zero and stable rank one. We show that the space of extremal quasitraces
and the scale of $A$ contain enough information to determine whether $M(A)/A$
is extrem... | math |
2,359 | Regularity of operators on essential extensions of the compacts | math.OA | A semiregular operator on a Hilbert C^*-module, or equivalently, on the
C^*-algebra of `compact' operators on it, is a closable densely defined
operator whose adjoint is also densely defined. It is shown that for operators
on extensions of compacts by unital or abelian C^*-algebras, semiregularity
leads to regularity. ... | math |
2,360 | Pure infiniteness, stability and C*-algebras of graphs and dynamical systems | math.OA | Pure infiniteness (in sense of E.Kirchberg and M.R{\o}rdam) is considered for
C*-algebras arising from singly generated dynamical systems. In particular,
Cuntz-Krieger algebras and their generalizations, i.e., graph-algebras and O_A
of an infinite matrix A, admit characterizations of pure infiniteness. As a
consequence... | math |
2,361 | Topological Entropy for the Canonical Endomorphism of Cuntz-Krieger Algebras | math.OA | It is shown that Voiculescu's toplogical entropy for the canonical
endomorphism of a simple Cuntz-Krieger algebra O_A equals the logarithm of the
spectral radius of A. | math |
2,362 | On the Toeplitz algebras of right-angled and finite-type Artin groups | math.OA | The graph product of a family of groups lies somewhere between their direct
and free products, with the graph determining which pairs of groups commute and
which do not. We show that the graph product of quasi-lattice ordered groups is
quasi-lattice ordered, and, when the underlying groups are amenable, that it
satisfi... | math |
2,363 | On unbounded p-summable Fredholm modules | math.OA | We prove that odd unbounded p-summable Fredholm modules are also bounded
p-summable Fredholm modules (this is the odd counterpart of a result of A.
Connes for the case of even Fredholm modules). | math |
2,364 | Hilbert bimodules with involution | math.OA | We examine Hilbert bimodules which possess a (generally unbounded)
involution. Topics considered include a linking algebra representation,
duality, locality, and the role of these bimodules in noncommutative
differential geometry. | math |
2,365 | On $C^*$-algebras related to asymptotic homomorphisms | math.OA | We study the $C^*$-algebras related to Mishchenko's version of asymptotic
homomorphisms. In particular we show that their different versions are weakly
homotopy equivalent but not isomorphic to each other. We give also the
continuous version for these algebras. | math |
2,366 | Interactions in noncommutative dynamics | math.OA | A mathematical notion of interaction is introduced for noncommutative
dynamical systems, i.e., for one parameter groups of *-automorphisms of $\Cal
B(H)$ endowed with a certain causal structure. With any interaction there is a
well-defined "state of the past" and a well-defined "state of the future". We
describe the co... | math |
2,367 | Exactness of reduced amalgamated free product C*-algebras | math.OA | Some completely positive maps on reduced amalgamated free products of
C*-algebras are constructed; these allow a proof that the class of exact unital
C*-algebras is closed under taking reduced amalgamated free products.
Consequently, the class of exact discrete groups is closed under taking
amalgamated free products. | math |
2,368 | Exactness of Cuntz-Pimsner C*-algebras | math.OA | Let H be a full Hilbert bimodule over a C*-algebra A. We show that the
Cuntz-Pimsner C*-algebra associated to H is exact if and only if A is exact.
Using this result, we give alternative proofs for exactness of reduced
amalgamated free products of exact C*-algebras. In the case that A is a finite
dimensional C*-algebra... | math |
2,369 | Purely infinite, simple C*-algebras arising from free product constructions, II | math.OA | Certain reduced free products of C*-algebras,
(A,phi)=(A_1,phi_1)*(A_2,\phi_2), taken with respect to faithful states, at
least one of which is not a trace, are shown to be purely infinite and simple.
It is assumed that one of the A_i contain a partial isometry in the spectral
subspace of phi_i corresponding to a posit... | math |
2,370 | Purely infinite, simple C*-algebras arising from free product constructions, III | math.OA | In the reduced free product of C*-algebras (A,phi)=(A_1,phi_1)*(A_2,phi_2), A
is shown to be purely infinite and simple under the hypothesis that A_1 is the
crossed product of a C*-algebra by a discrete infinite group, phi_1 is well
behaved with respect to this crossed product and A_2 is not one dimensional. | math |
2,371 | Projections in free product C*-algebras, II | math.OA | Let (A,phi) be the reduced free product of infinitely many pairs (A_i,phi_i)
of C*-algebras with faithful states. Assume that the A_i are not too small, in
a specific sense. It is shown that if phi is a trace then K_0(A) is determined
entirely by K_0(phi). If, furthermore, the image of K_0(phi) is dense in the
reals th... | math |
2,372 | Topological entropy of some automorphisms of reduced amalgamated free product C*-algebras | math.OA | Certain classes of automorphisms of recued amalgamated free products of
C*-algebras are shown to have Brown-Voiculescu topological entropy zero. Also,
for automorphisms of exact C*-algebras, the Connes-Narnhofer-Thirring entropy
is shown to be bounded above by the Brown-Voiculescu entropy. These facts are
applied to ge... | math |
2,373 | Compressions of free products of von Neumann algebras | math.OA | A reduction formula for compressions of von Neumann algebras arising as free
products is proved. This shows that the fundamental group is all of the
positive reals for some such algebras. Additionally, by taking a sort of free
product with an unbounded semicircular element, continuous one parameter groups
of trace scal... | math |
2,374 | Embeddings of reduced free products of operator algebras | math.OA | Given reduced amalgamated free products of C$^*$-algebras,
$(A,phi)=*_i(A_i,phi_i)$ and $(D,psi)=*_i(D_i,psi_i)$, an embedding $A\to D$ is
shown to exist assuming there are conditional expectation preserving embeddings
$A_i\to D_i$. This result is extended to show the existance of the reduced
amalgamated free product o... | math |
2,375 | Index of $Γ$-equivariant Toeplitz operators | math.OA | Let $\Gamma$ be a discrete icc subgroup of PSL(2,R) of infinite covolume. and
let M denote the quotient of the unit disc by $\Gamma$. We prove that a
Toeplitz operator with $\Gamma$-invariant symbol f in C(M) is Brauer Fredholm
if its symbol is invertible on the boundary of M and its Brauer index is equal
to the windin... | math |
2,376 | Homotopy of state orbits | math.OA | Let M be a von Neumann algebra, f a faithful normal state and denote by M^f
the fixed point algebra of the modular group of f. Let U_M and U_{M^f} be the
unitary groups of M and M^f. In this paper we study the quotient U_M/U_{M^f}
endowed with two natural topologies: the one induced by the usual norm of M
(called here ... | math |
2,377 | Geometry of oblique projections | math.OA | Let A be a unital C*-algebra. Denote by P the space of selfadjoint
projections of A. We study the relationship between P and the spaces of
projections P_a determined by the different involutions #_a induced by positive
invertible elements a in A. The maps f_p: P \to P_a sending p to the unique q
in P_a with the same ra... | math |
2,378 | The ideal structure of the Hecke C*-algebra of Bost and Connes | math.OA | We compute explicitly the primitive ideal space of the Bost-Connes Hecke
C*-algebra by embedding it as a full corner in a transformation group
C*-algebra and applying a general theorem of Williams. This requires the
computation of the quasi-orbit space for the action of the multiplicative
positive rationals on the spac... | math |
2,379 | From endomorphisms to automorphisms and back: dilations and full corners | math.OA | When S is a discrete subsemigroup of a discrete group G such that G = S^{-1}
S, it is possible to extend circle-valued multipliers from S to G; to dilate
(projective) isometric representations of S to (projective) unitary
representations of G; and to dilate/extend actions of S by injective
endomorphisms of a C*-algebra... | math |
2,380 | Projective spaces of a C*-algebra | math.OA | Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we
study the notion of projective space associated to a C*-algebra A with a fixed
projection p. The resulting space P(p) admits a rich geometrical structure as a
holomorphic manifold and a homogeneous reductive space of the invertible group
of A. ... | math |
2,381 | Polar decomposition under perturbations of the scalar product | math.OA | Let A be a unital C* algebra with involution * represented in a Hilbert space
H, G the group of invertible elements of A, U the unitary group of A, G^s the
set of invertible selfadjoint elements of A, Q={e in G : e^2 = 1} the space of
reflections and P = Q\cap U. For any positive a in G consider the a-unitary
group U_a... | math |
2,382 | Orbits of conditional expectations | math.OA | Let N \subseteq M be von Neumann algebras and E:M\to N a faithful normal
conditional expectation. In this work it is shown that the similarity orbit
S(E) of E by the natural action of the invertible group of G_M of M has a
natural complex analytic structure and the map given by this action: G_M\to
S(E) is a smooth prin... | math |
2,383 | Projective space of a C*-module | math.OA | Let X be a right Hilbert C*-module over A. We study the geometry and the
topology of the projective space P(X) of X, consisting of the orthocomplemented
submodules of X which are generated by a single element. We also study the
geometry of the p-sphere S_p(X) and the natural fibration S_p(X) \to P(X),
where S_p(X)={x\i... | math |
2,384 | Inclusions of second quantization algebras | math.OA | In this note we study inclusions of second quantization algebras, namely
inclusions of von Neumann algebras on the Fock space of a separable complex
Hilbert space H, generated by the Weyl unitaries with test functions in closed,
real linear subspaces of H. We show that the class of irreducible inclusions of
standard se... | math |
2,385 | Asymptotically split extensions and E-theory | math.OA | We show that the E-theory of Connes and Higson can be formulated in terms of
C*-extensions in a way quite similar to the way in which the KK-theory of
Kasparov can. The essential difference is that the role played by split
extensions should be taken by asymptotically split extensions. We call an
extension of a C*-algeb... | math |
2,386 | Universal C*-algebra of real rank zero | math.OA | It is well-known that every commutative separable unital C*-algebra of real
rank zero is a quotient of the C*-algebra of all compex continous functions
defined on the Cantor cube. We prove a non-commutative version of this result
by showing that the class of all separable unital C*-algebras of real rank zero
concides w... | math |
2,387 | Microstates free entropy and cost of equivalence relations | math.OA | We define an analog of Voiculescu's free entropy for n-tuples of unitaries
(u_{1},...,u_{n}) in a tracial von Neumann algebra M, normalizing a unital
diffuse abelian subalgebra B in M. Using this quantity, we define the free
dimension \delta_{0}(u_{1},..,u_{n}\btw B). This number depends on (u_{1},...
,u_{n}) only up `... | math |
2,388 | Three Bimodules for Mansfield's Imprimitivity Theorem | math.OA | There are at least three imprimitivity bimodules naturally associated to a
maximal coaction of a discrete group G on a C*-algebra and a normal subgroup of
G: Mansfield's bimodule; the bimodule assembled by Ng from Green's
imprimitivity bimodule and Katayama duality; and a bimodule assembled from
Green's bimodule and a ... | math |
2,389 | Naturality and Induced Representations | math.OA | We show that induction of covariant representations for C*-dynamical systems
is natural in the sense that it gives a natural transformation between certain
crossed-product functors. This involves setting up suitable categories of
C*-algebras and dynamical systems, and extending the usual constructions of
crossed produc... | math |
2,390 | Entropy of Bogoliubov automorphisms of CAR and CCR algebras with respect to quasi-free states | math.OA | We compute the dynamical entropy of Bogoliubov automorphisms of CAR and CCR
algebras with respect to arbitrary gauge-invariant quasi-free states. This
completes the research started by Stormer and Voiculescu, and continued in
works of Narnhofer-Thirring and Park-Shin. | math |
2,391 | On the K-property of quantized Arnold cat maps | math.OA | We prove that some quantized Arnold cat maps are entropic K-systems. This
result was formulated by H. Narnhofer[1], but the fact that the optimal
decomposition for the multi-channel entropy constructed there is not strictly
local was not appropriately taken care of. We propose a strictly local
decomposition based on a ... | math |
2,392 | Entropy in type I algebras | math.OA | It is shown that if (M,phi,alpha) is a W*-dynamical system with M a type I
von Neumann algebra then the entropy of alpha w.r.t. phi equals the entropy of
the restriction of alpha to the center of M. If furthermore (N,psi,beta) is a
W*-dynamical system with N injective then the entropy of the tensor product
system is th... | math |
2,393 | Entropy of automorphisms of II_1-factors arising from the dynamical systems theory | math.OA | Let a countable amenable group G acts freely and ergodically on a Lebesgue
space (X,mu), preserving the measure mu. If T is an automorphism of the
equivalence relation defined by G then T can be extended to an automorphism
alpha_T of the II_1-factor M=L^\infty(X,\mu)\rtimes G. We prove that if T
commutes with the actio... | math |
2,394 | Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theorem | math.OA | For each \beta\in(0,+\infty) there exists a canonical measure \mu_\beta on
the ring A_f of finite adeles. We show that the positive rationals act
ergodically on (A_f,\mu_\beta) for \beta\in(0,1], and then deduce from this the
uniqueness of KMS_\beta-states for the Bost-Connes system. | math |
2,395 | Asymptotic homomorphisms into the Calkin algebra | math.OA | Let $A$ be a separable $C^*$-algebra and let $B$ be a stable $C^*$-algebra
with a strictly positive element. We consider the (semi)group $\Ext^{as}(A,B)$
(resp. $\Ext(A,B)$) of homotopy classes of asymptotic (resp. of genuine)
homomorphisms from $A$ to the corona algebra $M(B)/B$ and the natural map
$i:\Ext(A,B)\ar\Ext... | math |
2,396 | Dual group actions on C*-algebras and their description by Hilbert extensions | math.OA | Given a C*-algebra $A$, a discrete abelian group $X$ and a homomorphism
$\Theta: X\to$ Out$A$ defining the dual action group $\Gamma\subset$ aut$A$,
the paper contains results on existence and characterization of Hilbert
$\{A,\Gamma\}$, where the action is given by $\hat{X}$. They are stated at the
(abstract) C*-level ... | math |
2,397 | Serre-Swan theorem for non-commutative C$^{*}$-algebras | math.OA | We generalize the Serre-Swan theorem to non-commutative C$^{*}$-algebras. For
a Hilbert C$^{*}$-module $X$ over a C$^{*}$-algebra ${\cal A}$, we introduce a
hermitian vector bundle $\exx$ associated to $X$. We show that there is a
linear subspace $\Gamma_{X}$ of the space of all holomorphic sections of ${\cal
E}_{X}$ a... | math |
2,398 | Boundary actions for affine buildings and higher rank Cuntz-Krieger algebras | math.OA | Let $\G$ be a group of type rotating automorphisms of an affine building
$\cB$ of type $\wt A_2$. If $\G$ acts freely on the vertices of $\cB$ with
finitely many orbits, and if $\Omega$ is the (maximal) boundary of $\cB$, then
$C(\Om)\rtimes \G$ is a p.i.s.u.n. $C^*$-algebra. This algebra has a structure
theory analogo... | math |
2,399 | The generalized Chern character and Lefschetz numbers in W*-modules | math.OA | We define N-theory being some analogue of K-theory on the category of von
Neumann algebras such that $K_0(A)\subset N_0(A)$ for any von Neumann algebra
A. Moreover, it turns out to be possible to construct the extension of the
Chern character to some homomorphism from $N_0(A)$ to even Banach cyclic
homology of A. Also,... | math |
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