| 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 | |