OAI/Topology/CoarseAssembly/CoefficientIsometry.lean

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9 declarations, 0 contain sorry, 0 declared as axioms

Isometric changes of the coefficient Hilbert space

Changing coefficients by a pointwise isometry preserves propagation. Extending by the identity on its orthogonal complement preserves compact square defects, as required to place localized cycles on an ample module.

  1. theorem OAI.CoarseAssembly.DiscreteRoe.coefficientIsometry_apply line 23
  2. theorem OAI.CoarseAssembly.DiscreteRoe.coefficientIsometry_adjoint_apply line 27
  3. theorem OAI.CoarseAssembly.DiscreteRoe.coefficientIsometry_adjoint_single line 34
  4. theorem OAI.CoarseAssembly.DiscreteRoe.coefficientConjugation_entry line 42
  5. theorem OAI.CoarseAssembly.DiscreteRoe.coefficientConjugation_propagation line 52
  6. theorem OAI.CoarseAssembly.DiscreteRoe.coefficientExtension_selfAdjoint line 60
  7. theorem OAI.CoarseAssembly.DiscreteRoe.coefficientExtension_norm_le line 65
  8. theorem OAI.CoarseAssembly.DiscreteRoe.coefficientExtension_square_compact line 69
  9. theorem OAI.CoarseAssembly.DiscreteRoe.coefficientExtension_propagation line 74