Theorems · Definition · functional analysis

WeakDual.CharacterSpace.equivAlgHom

{𝕜 : Type u_1} →
  {A : Type u_2} →
    [inst : NontriviallyNormedField 𝕜] →
      [inst_1 : NormedRing A] →
        [CompleteSpace A] → [inst_3 : NormedAlgebra 𝕜 A] → ↑(WeakDual.characterSpace 𝕜 A) ≃ (A →ₐ[𝕜] 𝕜)

The equivalence between characters and algebra homomorphisms into the base field.

Defined in

Mathlib.Analysis.Normed.Algebra.Spectrum

Cited by

4 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedRingCompleteSpaceNormedAlgebra