OAI/Analysis/KadisonKastler/MatrixCentralCone.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

Matrix corner maps preserve the generated positive cone

Both directions of the corner partial isometry are positive sums of modular quadratic operators. The central-vector projection therefore preserves this cone as well.

  1. theorem OAI.KadisonKastler.complex_ofReal_smul line 24
  2. theorem OAI.KadisonKastler.modularPositiveCone_sum_mem line 27
  3. theorem OAI.KadisonKastler.matrixCentralColumn_preserves_positiveCone line 46
  4. theorem OAI.KadisonKastler.matrixCentralColumn_star_preserves_positiveCone line 60
  5. theorem OAI.KadisonKastler.matrixCentralProjection_preserves_positiveCone line 81