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Many changes to entry `Complex_Bounded_Operators`:

Description

Many changes to entry Complex_Bounded_Operators:

  • Removed all use of deprecated ⟨.,.⟩ syntax for complex inner product. (Now: ∙⇩C)
  • Cosmetic changes and cleanup of some proofs
  • Type class one_dim inherits from complex_inner now.
  • Moved various theorems around between theories
  • Added [simp] to: Proj_partial_isometry, cadjoint_id
  • Removed theorems: onorm_Inf_bound, norm_unit_sphere
  • Changed theorems: of_complex_cblinfun_apply (made into more general simp-rule), TODO orthospacething
  • New definition: rank1 (and lemmas about it)
  • New theorems: one_dim_iso_cblinfun_apply, vector_to_cblinfun_one_dim_iso, image_vector_to_cblinfun_adj, image_vector_to_cblinfun_adj', sgn_cinner, orthocomplement_top, orthogonal_spaces_ccspan, norm_scaleC_sgn, one_dim_ccsubspace_all_or_nothing, surj_isometry_is_unitary
  • Renamed vector_to_cblinfun_cblinfun_apply -> vector_to_cblinfun_cblinfun_compose (also turned around and added [simp]), cancel_apply_Proj -> Proj_fixes_image, range_is_clinear -> range_is_csubspace.
  • Changed definition: is_Proj (logically equivalent by Proj_range_closed)

Fixed entry Registers due to the changes above.

Details

Provenance
Dominique Unruh <unruh@ut.ee>Authored on
Parents
rAFPa74db29363f5: tuned proofs
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