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9eeb9c7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | import OAI.Analysis.IrrationalRotation.Rotation.Rotation
import OAI.Analysis.IrrationalRotation.Model.ConcreteSpectral
namespace OAI
/-! Continuous circle weights with invariant-projection and spectral properties. -/
namespace Invariant233
def Rotation.IsContinuousCounterexample (θ : ℝ) (f : C(Circle, ℝ)) : Prop :=
IsContinuousCircleWeight f ∧
let operator : Rotation.Hilbert →L[ℂ] Rotation.Hilbert := Rotation.weightedReal θ f
let factor : VonNeumannAlgebra Rotation.Hilbert := Rotation.algebra θ
operator ∈ factor ∧
HasOnlyTrivialInvariantProjections (H := Rotation.Hilbert) factor operator ∧
operator ≠ 0 ∧
NormQuasinilpotent (A := Rotation.Hilbert →L[ℂ] Rotation.Hilbert) operator ∧
vectorFugledeKadisonDeterminant (H := Rotation.Hilbert) Rotation.vacuum operator = 0
end Invariant233
end OAI
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