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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 24 | import OAI.Analysis.IrrationalRotation.Model.Commutant
import OAI.Analysis.IrrationalRotation.Model.OperatorProperties
import Mathlib.LinearAlgebra.FiniteDimensional.Basic
namespace OAI
noncomputable section
namespace Invariant233
variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]
def IsHyperfinite (M : VonNeumannAlgebra H) : Prop :=
∃ A : ℕ → StarSubalgebra ℂ (H →L[ℂ] H), Monotone A ∧
(∀ n, A n ≤ M.toStarSubalgebra) ∧
(∀ n, FiniteDimensional ℂ (A n)) ∧
closure {B : H →Lₚₜ[ℂ] H | ∃ n, strongOperatorUnderlying B ∈ A n} =
{B : H →Lₚₜ[ℂ] H | strongOperatorUnderlying B ∈ M}
end Invariant233
end
end OAI
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