Theorems · Theorem · functional analysis

NonUnitalStarAlgHom.ext_continuousMap

∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : Nontrivial R] [inst_2 : StarRing R]
  [inst_3 : MetricSpace R] [inst_4 : IsTopologicalSemiring R] [inst_5 : ContinuousStar R] [inst_6 : NonUnitalRing A]
  [inst_7 : StarRing A] [inst_8 : TopologicalSpace A] [inst_9 : Module R A] [inst_10 : IsScalarTower R A A]
  [inst_11 : SMulCommClass R A A] [ContinuousMapZero.UniqueHom R A] (a : A) [CompactSpace ↑(quasispectrum R a)]
  (φ ψ : ContinuousMapZero (↑(quasispectrum R a)) R →⋆ₙₐ[R] A),
  Continuous ⇑φ →
    Continuous ⇑ψ → φ (ContinuousMapZero.id (quasispectrum R a)) = ψ (ContinuousMapZero.id (quasispectrum R a)) → φ = ψ

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNontrivialStarRingMetricSpaceIsTopologicalSemiringContinuousStarNonUnitalRingStarRingTopologicalSpaceModuleIsScalarTowerSMulCommClassContinuousMapZero.UniqueHomCompactSpace