OAI/Analysis/KadisonKastler/CornerPullbackVectors.lean

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7 declarations, 0 contain sorry, 0 declared as axioms

Faithful vector states implementing the corner pullbacks

Pulling a normalized corner state back by an isometry gives a normalized faithful vector state on the original represented factor. This avoids an extra representation assumption in the corner homogeneity application.

  1. theorem OAI.KadisonKastler.isometry_sandwich_cancel line 22
  2. theorem OAI.KadisonKastler.isometry_pullback_vector_separating line 28
  3. theorem OAI.KadisonKastler.isometry_pullback_norm_sq line 38
  4. theorem OAI.KadisonKastler.vectorFunctional_real_smul line 45
  5. theorem OAI.KadisonKastler.vectorFunctional_normalize line 56
  6. theorem OAI.KadisonKastler.normalized_isometry_pullback_separating line 61
  7. theorem OAI.KadisonKastler.vectorCornerState_pullback line 74