OAI/Analysis/OperatorAlgebra/CyclicGNSUnitary.lean

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8 declarations, 0 contain sorry, 0 declared as axioms

The concrete cyclic vector realization of a positive functional is unitarily equivalent to its GNS space.

  1. def OAI.WeakPureInfiniteness.cyclicPreGNSIsometry line 19
  2. def OAI.WeakPureInfiniteness.cyclicGNSIsometry line 30
  3. lemma OAI.WeakPureInfiniteness.cyclicGNSIsometry_coe line 33
  4. lemma OAI.WeakPureInfiniteness.cyclicGNSIsometry_vector line 38
  5. theorem OAI.WeakPureInfiniteness.cyclicGNSIsometry_surjective line 42
  6. def OAI.WeakPureInfiniteness.cyclicGNSUnitary line 55
  7. theorem OAI.WeakPureInfiniteness.cyclicGNSIsometry_intertwines line 59
  8. theorem OAI.WeakPureInfiniteness.cyclicGNSUnitary_conjugates line 71