Theorems · Theorem · functional analysis
gelfandTransform_map_star
∀ {A : Type u_1} [inst : CommCStarAlgebra A] (a : A),
(WeakDual.gelfandTransform ℂ A) (star a) = star ((WeakDual.gelfandTransform ℂ A) a)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommCStarAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 7,166
- Complexstatement and proof · cited by 5,565
- AlgHomstatement · cited by 3,236
- ContinuousMapstatement · cited by 2,491
- Star.starstatement · cited by 1,082
- WeakDualstatement · cited by 103
- ContinuousMap.extproof · cited by 92
- WeakDual.characterSpacestatement and proof · cited by 39
- StarHomClass.map_starproof · cited by 20
- CommCStarAlgebrastatement and proof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- gelfandStarTransformproof · cited by 5
- gelfandTransform_isometryproof · cited by 2
- gelfandStarTransform_symm_applystatement · cited by 0