OAI/Analysis/KadisonKastler/CentralAveragingLimit.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

Norm convergence of iterated central averaging

  1. theorem OAI.KadisonKastler.exists_central_mem_closed_orbit line 19

    Source documentation

    Geometric refinement makes the central corrections summable and produces an actual central element in the norm-closed unitary orbit hull.

    theorem exists_central_mem_closed_orbit (x : Algebra M) :
        ∃ c : Algebra (concreteCenter M),
          c.val ∈ closure (convexHull ℝ (innerUnitaryOrbit M x.val)) := by
    …

    Mentions: OAI.KadisonKastler.Algebra, OAI.KadisonKastler.concreteCenter, OAI.KadisonKastler.innerUnitaryOrbit

  2. theorem OAI.KadisonKastler.publishedDixmierAveraging line 107

    Source documentation

    The exact published averaging input, in every represented von Neumann algebra.

    theorem publishedDixmierAveraging (N : VonNeumannAlgebra H) : PublishedDixmierAveraging N := by
    …

    Mentions: OAI.KadisonKastler.PublishedDixmierAveraging