File size: 940 Bytes
67aee1d | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | 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
|