OAI/Analysis/KadisonKastler/WeakMapCompact.lean

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4 declarations, 0 contain sorry, 0 declared as axioms

The completely bounded ball is compact in the pointwise weak operator topology.

  1. structure OAI.KadisonKastler.BoundedWeakAlgebraMap line 22
  2. def OAI.KadisonKastler.boundedWeakAlgebraCoefficients line 26
  3. instance OAI.KadisonKastler.boundedWeakAlgebraMapTopology line 30
  4. theorem OAI.KadisonKastler.isCompact_boundedWeakAlgebraMap line 35

    Source documentation

    All matrix bounds are retained at a pointwise weak cluster point.

    theorem isCompact_boundedWeakAlgebraMap (M : VonNeumannAlgebra H) {c : ℝ} (hc : 0 ≤ c) :
        IsCompact (Set.univ : Set (BoundedWeakAlgebraMap M c)) := by
    …

    Mentions: OAI.KadisonKastler.BoundedWeakAlgebraMap