Theorems · Theorem · functional analysis
cfc_eq_cfcL_mkD
∀ {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 : TopologicalSpace A] [inst_6 : Ring A]
[inst_7 : StarRing A] [inst_8 : Algebra R A] [instCFC : ContinuousFunctionalCalculus R A p] (f : R → R) (a : A)
(ha : autoParam (p a) _auto_113✝), cfc f a = (cfcL ha) (ContinuousMap.mkD ((spectrum R a).domRestrict f) 0)A version of cfc_eq_cfcL in terms of ContinuousMapZero.mkD
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
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
- TopologicalSpacestatement and proof · cited by 24,529
- RingHom.idstatement · cited by 18,349
- 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
- ContinuousLinearMapstatement · cited by 5,352
- ContinuousMapstatement · cited by 2,491
- StarRingstatement and proof · cited by 1,686
- MetricSpacestatement and proof · cited by 1,684
Cited by2
Results whose statement or proof uses this declaration.
- integrable_cfc'proof · cited by 2
- cfc_integral'proof · cited by 2