Theorems · Theorem · functional analysis
gelfandTransform_bijective
∀ (A : Type u_1) [inst : CommCStarAlgebra A], Function.Bijective ⇑(WeakDual.gelfandTransform ℂ A)
The Gelfand transform is bijective when the algebra is a C⋆-algebra over ℂ.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 304 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.
Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by2
Results whose statement or proof uses this declaration.
- gelfandStarTransformproof · cited by 5
- gelfandStarTransform_symm_applystatement · cited by 0