OAI/Analysis/KadisonKastler/TypeIIICyclicSeparating.lean

GitHub source file

3 declarations, 0 contain sorry, 0 declared as axioms

Cyclic separating vectors in the original type III representation

The cyclic restriction of a separating vector has an infinite commutant corner: its modular conjugation carries a proper isometry into that corner. Projection comparison then moves the cyclic subspace onto the original Hilbert space, while preserving separation and the vector norm.

  1. theorem OAI.KadisonKastler.ModularConjugationData.isometry_surjective_of_commutant_finite line 25
  2. theorem OAI.KadisonKastler.cyclicOrbitProjection_not_finite line 47
  3. theorem OAI.KadisonKastler.TypeIIIFactor.exists_cyclic_separating_unit_vector line 75