OAI/Analysis/OperatorAlgebra/ScalarOperatorSlices.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

Scalar L² slices characterize commutation in the amplification. In particular, commutation with the represented C*-algebra automatically extends to its concrete bicommutant, without assuming normality of any expectation.

  1. def OAI.WeakPureInfiniteness.scalarOperatorSlice line 20
  2. lemma OAI.WeakPureInfiniteness.scalarOperatorSlice_inner line 23
  3. lemma OAI.WeakPureInfiniteness.scalarOperatorSlice_mul_pointwise line 32
  4. lemma OAI.WeakPureInfiniteness.scalarOperatorSlice_pointwise_mul line 43
  5. theorem OAI.WeakPureInfiniteness.pointwise_commute_iff_slices line 60
  6. theorem OAI.WeakPureInfiniteness.pointwise_commutation_extends_bicommutant line 78