| 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 | |