| import Mathlib | |
| import OAI.Analysis.FreeWords.HaarEndpointsDefinitions | |
| import OAI.Analysis.FreeWords.MatrixConditionalExpectation | |
| namespace OAI | |
| noncomputable section | |
| namespace KKMatrixBounds | |
| noncomputable section | |
| open KKHaarEndpoints KKMatrixExpectation Filter | |
| open scoped Matrix.Norms.Operator Topology | |
| variable {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] | |
| def wordBound (n:ℕ) (w:List (ℤ×Matrix (Fin n) (Fin n) A)) : ℝ := | |
| (w.map fun z => (n:ℝ)*‖z.2‖).prod | |
| def AmplifiedBlockBounds : Prop := | |
| (∀n:ℕ,∀U:unitary (Matrix (Fin n) (Fin n) A),∀w:List (ℤ×Matrix (Fin n) (Fin n) A), | |
| ‖powerWord U w‖≤wordBound n w) ∧ | |
| (∀(ι:Type) (L:Filter ι) (τ:A →ₗ[ℂ] ℂ) (n:ℕ) | |
| (X:ι → Matrix (Fin n) (Fin n) A), | |
| (∀a b,Tendsto (fun j => τ (X j a b)) L (𝓝 0)) → | |
| Tendsto (fun j => matrixExpectation τ n (X j)) L (𝓝 0)) | |
| end | |
| end KKMatrixBounds | |
| end | |
| end OAI | |