OAI/Analysis/KadisonKastler/WeakMapCompact.lean
4 declarations, 0 contain sorry, 0 declared as axioms
The completely bounded ball is compact in the pointwise weak operator topology.
- structure
OAI.KadisonKastler.BoundedWeakAlgebraMapline 22 - def
OAI.KadisonKastler.boundedWeakAlgebraCoefficientsline 26 - instance
OAI.KadisonKastler.boundedWeakAlgebraMapTopologyline 30 - theorem
OAI.KadisonKastler.isCompact_boundedWeakAlgebraMapline 35Source 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