OAI/Analysis/OperatorAlgebra/ScalarLpContinuousCutoffs.lean

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11 declarations, 0 contain sorry, 0 declared as axioms

Continuous functional calculus for scalar L² multiplication, in a form that keeps pointwise cutoffs and their operator realizations connected.

  1. instance OAI.WeakPureInfiniteness.scalarBoundedContinuousCStarAlgebra line 18
  2. instance OAI.WeakPureInfiniteness.scalarBoundedContinuousComplexCFC line 21
  3. instance OAI.WeakPureInfiniteness.scalarBoundedContinuousRealCFC line 25
  4. def OAI.WeakPureInfiniteness.boundedFunctionEval line 29
  5. def OAI.WeakPureInfiniteness.scalarCosine line 38
  6. lemma OAI.WeakPureInfiniteness.scalarCosine_apply line 44
  7. lemma OAI.WeakPureInfiniteness.scalarCosine_selfAdjoint line 47
  8. lemma OAI.WeakPureInfiniteness.scalarCosine_character line 53
  9. lemma OAI.WeakPureInfiniteness.scalarCosine_cfc_apply line 64
  10. lemma OAI.WeakPureInfiniteness.scalarLp_commute_cosine line 75
  11. lemma OAI.WeakPureInfiniteness.scalarLp_commute_cosine_cfc line 90