OAI/Analysis/KadisonKastler/BicentralizerExpectation.lean

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8 declarations, 0 contain sorry, 0 declared as axioms

The state-preserving bicentralizer retraction

The constructed contractive projection has the actual bicentralizer as codomain. Tomiyama's projection identities make it bimodular; normality is not required.

  1. theorem OAI.KadisonKastler.stateBicentralizerVonNeumann_le line 22
  2. def OAI.KadisonKastler.bicentralizerExpectation line 26
  3. theorem OAI.KadisonKastler.bicentralizerExpectation_val line 35
  4. theorem OAI.KadisonKastler.bicentralizerExpectation_norm_le line 39
  5. theorem OAI.KadisonKastler.bicentralizerExpectation_fixed line 46
  6. theorem OAI.KadisonKastler.bicentralizerExpectation_bimodule line 56
  7. theorem OAI.KadisonKastler.bicentralizerExpectation_state line 70
  8. theorem OAI.KadisonKastler.bicentralizerExpectation_faithful line 75