OAI/Analysis/Nuclearity/CPWeakOperatorUltralimit.lean

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A uniformly contractive family of cpc maps into Hilbert-space operators has a cpc weak operator ultralimit. Complete positivity is checked on each finite matrix and finite vector family, by passing the positive quadratic forms to their scalar limits.

  1. lemma OAI.WeakPureInfiniteness.cpcOperatorFamily_bound line 22
  2. def OAI.WeakPureInfiniteness.cpOperatorUltraLinear line 27
  3. def OAI.WeakPureInfiniteness.cpOperatorUltraLimit line 52
  4. lemma OAI.WeakPureInfiniteness.cpOperatorUltraLimit_norm_le line 61
  5. lemma OAI.WeakPureInfiniteness.cpOperatorUltraLimit_inner_tendsto line 66
  6. lemma OAI.WeakPureInfiniteness.matrixOperator_inner_formula line 73
  7. lemma OAI.WeakPureInfiniteness.cpOperatorUltraLimit_completelyPositive line 79