Theorems · Theorem · functional analysis
continuousFunctionalCalculus_map_id
∀ {A : Type u_1} [inst : CStarAlgebra A] (a : A) [inst_1 : IsStarNormal a],
(continuousFunctionalCalculus a) (ContinuousMap.restrict (spectrum ℂ a) (ContinuousMap.id ℂ)) = ⟨a, ⋯⟩- Cited by
- 1 results in Mathlib
- Foundations
- Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebraIsStarNormal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Set.Elemstatement · cited by 7,166
- Complexstatement and proof · cited by 5,565
- ContinuousMapstatement · cited by 2,491
- spectrumstatement · cited by 510
- StarSubalgebrastatement · cited by 194
- StarAlgEquivstatement · cited by 132
- CStarAlgebrastatement and proof · cited by 123
- IsStarNormalstatement and proof · cited by 117
- ContinuousMap.idstatement · cited by 73
- ContinuousMap.restrictstatement · cited by 61
Cited by1
Results whose statement or proof uses this declaration.
- cfcHom_eq_of_isStarNormalproof · cited by 0