OAI/Analysis/KadisonKastler/DirectIntegralConjugacy.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

Assembling fiber conjugacies on the actual direct-integral space

OperatorFieldDecomposition records the decomposition and reconstruction properties of a given constant-fiber direct integral. It is data, not a published theorem or an existence assertion. The assembly argument below uses actual multiplication unitaries on L²(X,H).

  1. def OAI.KadisonKastler.RepresentsOperatorField line 23
  2. theorem OAI.KadisonKastler.RepresentsOperatorField.unique line 28
  3. structure OAI.KadisonKastler.OperatorFieldDecomposition line 35
  4. theorem OAI.KadisonKastler.operatorField_conjugation_inclusion line 45
  5. theorem OAI.KadisonKastler.conjugates_regularUnitaryField line 82