OAI/Analysis/KadisonSimilarity/Similarity/CyclicSimilarity.lean

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4 declarations, 0 contain sorry, 0 declared as axioms

A positive functional comparable to a cyclic orbit gives an actual invertible intertwiner with its GNS representation.

  1. def OAI.KadisonSimilarity.boundedHomOrbit line 18
  2. theorem OAI.KadisonSimilarity.boundedHomOrbit_apply line 22
  3. theorem OAI.KadisonSimilarity.similarity_of_cyclic_orbit_sandwich line 25
  4. theorem OAI.KadisonSimilarity.cyclic_similarity line 80

    Source documentation

    Every bounded cyclic representation is similar to a star representation. The proof uses only the established little Grothendieck estimate and GNS.

    theorem cyclic_similarity (π : BoundedUnitalHom A H) (ξ : H)
    (hcyc : DenseRange (fun a : A => π.1 a ξ)) : SimilarToStar A H π := by
…

    Mentions: OAI.KadisonSimilarity.BoundedUnitalHom, OAI.KadisonSimilarity.SimilarToStar