OAI/Analysis/KadisonKastler/FaithfulTensorFaithfulness.lean

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Faithfulness of the tensor restriction

Vector slices of a positive product operator lie in the original algebra. The faithful cyclic compression detects each such slice. Applying this to T* T proves faithfulness on the whole spatial von Neumann product.

  1. theorem OAI.KadisonKastler.tensorVectorSlice_eq_zero_of_faithfulTensorHom_eq_zero line 23
  2. theorem OAI.KadisonKastler.faithfulTensorHom_injective line 48
  3. theorem OAI.KadisonKastler.faithfulTensorHom_norm line 73