OAI/Analysis/KadisonKastler/RelativeCentralVectorDensity.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

The relative commutant is cyclic on the central-vector space

Compressing an algebra orbit by the finite central-vector projection is exactly the matrix relative-commutant average. Density on the original space therefore gives density on the central-vector space.

  1. def OAI.KadisonKastler.matrixRelativeAverage line 25

    Source documentation

    The actual algebra element obtained by finite matrix averaging.

    def matrixRelativeAverage (a : Algebra M) : Algebra E.relativeVonNeumann :=
…

    Mentions: OAI.KadisonKastler.Algebra

  2. theorem OAI.KadisonKastler.matrixRelativeAverage_apply line 30
  3. theorem OAI.KadisonKastler.matrixCentralProjection_algebraVector line 51
  4. theorem OAI.KadisonKastler.relative_algebra_orbit_mem_central line 79
  5. theorem OAI.KadisonKastler.relative_centralVector_orbit_dense line 96