OAI/Analysis/OperatorAlgebra/HilbertProjectionRange.lean

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8 declarations, 0 contain sorry, 0 declared as axioms

The range of an actual orthogonal projection as a complete Hilbert space, with its isometric inclusion recovering the original projection.

  1. def OAI.WeakPureInfiniteness.HilbertProjectionRange line 15
  2. instance OAI.WeakPureInfiniteness.hilbertProjectionRangeNorm line 17
  3. instance OAI.WeakPureInfiniteness.hilbertProjectionRangeInner line 20
  4. instance OAI.WeakPureInfiniteness.hilbertProjectionRangeComplete line 23
  5. def OAI.WeakPureInfiniteness.hilbertProjectionInclusion line 27
  6. lemma OAI.WeakPureInfiniteness.hilbertProjectionInclusion_fixed line 30
  7. lemma OAI.WeakPureInfiniteness.hilbertProjectionInclusion_adjoint line 38
  8. lemma OAI.WeakPureInfiniteness.hilbertProjectionInclusion_projection line 55