OAI/Analysis/KadisonKastler/CyclicRestriction.lean

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10 declarations, 0 contain sorry, 0 declared as axioms

Restricting a bounded representation to a cyclic orbit closure

The representation need not preserve the involution. Its cyclic orbit is a linear subspace, and its norm closure is invariant under each operator.

  1. def OAI.KadisonKastler.representationOrbitMap line 20
  2. def OAI.KadisonKastler.representationCyclicSpace line 25
  3. instance OAI.KadisonKastler.representationCyclicSpace_complete line 28
  4. theorem OAI.KadisonKastler.mem_representationCyclicSpace line 32
  5. theorem OAI.KadisonKastler.representationCyclicSpace_invariant line 38
  6. def OAI.KadisonKastler.representationCyclicVector line 51
  7. def OAI.KadisonKastler.restrictCyclicRepresentation line 54
  8. theorem OAI.KadisonKastler.restrictCyclicRepresentation_apply line 64
  9. theorem OAI.KadisonKastler.restrictCyclicRepresentation_cyclic line 68
  10. theorem OAI.KadisonKastler.norm_restrictCyclicRepresentation_le line 78