Theorems · Theorem · functional analysis
isometry_cfcHom
∀ {R : Type u_1} {A : Type u_2} {p : A → Prop} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : MetricSpace R]
[inst_3 : IsTopologicalSemiring R] [inst_4 : ContinuousStar R] [inst_5 : Ring A] [inst_6 : StarRing A]
[inst_7 : MetricSpace A] [inst_8 : Algebra R A] [inst_9 : IsometricContinuousFunctionalCalculus R A p] (a : A)
(ha : autoParam (p a) isometry_cfcHom._auto_1), Isometry ⇑(cfcHom ⋯)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Ringstatement and proof · cited by 7,463
- Set.Elemstatement · cited by 7,166
- ContinuousMapstatement · cited by 2,491
- StarRingstatement and proof · cited by 1,686
- MetricSpacestatement and proof · cited by 1,684
- ContinuousStarstatement and proof · cited by 543
- spectrumstatement · cited by 510
- IsTopologicalSemiringstatement and proof · cited by 442
Cited by4
Results whose statement or proof uses this declaration.
- norm_cfcHomproof · cited by 2
- lipschitzOnWith_cfc_funproof · cited by 1
- continuous_cfcHomSuperset_leftproof · cited by 1
- SpectrumRestricts.isometric_cfcproof · cited by 0