OAI/Analysis/KadisonSimilarity/Similarity/CompleteNorm.lean

GitHub source file

4 declarations, 0 contain sorry, 0 declared as axioms

The least nonnegative complete bound. Kirchberg's proof uses a similarity attaining this bound, rather than an arbitrary similarity.

  1. def OAI.KadisonSimilarity.completeNorm line 14
  2. theorem OAI.KadisonSimilarity.completeNorm_nonneg line 17
  3. theorem OAI.KadisonSimilarity.completeNorm_le line 21
  4. theorem OAI.KadisonSimilarity.completeBound_completeNorm line 26

    Source documentation

    Complete bounds form a closed set, so their finite infimum is a bound.

    theorem completeBound_completeNorm {f : A → (H →L[ℂ] H)}
    (hf : IsCompletelyBounded f) : CompleteBound f (completeNorm f) := by
…

    Mentions: OAI.KadisonSimilarity.IsCompletelyBounded, OAI.KadisonSimilarity.CompleteBound, OAI.KadisonSimilarity.completeNorm