Theorems · Theorem · functional analysis
gelfandTransform_isometry
∀ (A : Type u_1) [inst : CommCStarAlgebra A], Isometry ⇑(WeakDual.gelfandTransform ℂ A)
The Gelfand transform is an isometry when the algebra is a C⋆-algebra over ℂ.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 303 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.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- ENNRealproof · cited by 9,879
- Set.Elemstatement and proof · cited by 7,166
- Complexstatement and proof · cited by 5,565
- AlgHomstatement · cited by 3,236
- ContinuousMapstatement and proof · cited by 2,491
- iSupproof · cited by 2,415
- ENNReal.ofNNRealproof · cited by 1,279
- NNReal.toRealproof · cited by 1,260
- map_mulproof · cited by 1,137
- Star.starproof · cited by 1,082
Cited by2
Results whose statement or proof uses this declaration.
- CommCStarAlgebra.norm_add_eq_maxproof · cited by 3
- gelfandTransform_bijectiveproof · cited by 1