OAI/Analysis/KadisonSimilarity/Tracial/MatrixPopaPosition.lean

GitHub source file

4 declarations, 0 contain sorry, 0 declared as axioms

The fixed source factor is conjugated diagonally inside the prescribed matrix-subfactor ultrapower. Trace and inclusion properties follow from the concrete maps, with no operator-estimate hypothesis.

  1. def OAI.KadisonSimilarity.matrixConjugatedEmbedding line 35

    Source documentation

    The conjugate of the fixed source factor, diagonal in the matrix subfactor before passing to the tracial ultrapower.

    def matrixConjugatedEmbedding (u : unitary (Ultrapower τRn hRn ω trRn)) :
    R →⋆ₐ[ℂ] Ultrapower τBn hBn ω trBn :=
…
  2. theorem OAI.KadisonSimilarity.matrixConjugatedEmbedding_trace line 40
  3. theorem OAI.KadisonSimilarity.matrixConjugatedEmbedding_injective line 49
  4. theorem OAI.KadisonSimilarity.matrixConjugatedEmbedding_range_le line 57