OAI/Analysis/KadisonKastler/NestedScalarMeans.lean

GitHub source file

10 declarations, 0 contain sorry, 0 declared as axioms

Composing scalar means over two group coordinates

The row and outer means are bounded linear maps on actual L-infinity classes. Here we establish the algebraic and norm properties of their composition; the action identity is supplied by the commuting-coordinate construction.

  1. def OAI.KadisonKastler.nestedMeanRowsL line 24
  2. theorem OAI.KadisonKastler.nestedMeanRowsL_apply line 29
  3. def OAI.KadisonKastler.nestedScalarMeanL line 33
  4. theorem OAI.KadisonKastler.nestedMeanRowsL_norm_le line 37
  5. theorem OAI.KadisonKastler.nestedScalarMeanL_norm_le line 43
  6. theorem OAI.KadisonKastler.nestedMeanRowsL_const line 47
  7. theorem OAI.KadisonKastler.nestedScalarMeanL_const line 54
  8. theorem OAI.KadisonKastler.nestedScalarMeanL_positive line 60
  9. theorem OAI.KadisonKastler.nestedMeanRowsL_module line 69
  10. theorem OAI.KadisonKastler.nestedScalarMeanL_module line 83