Theorems · Theorem · functional analysis

IsSelfAdjoint.map_spectrum_real

∀ {F : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CStarAlgebra A] [inst_1 : CStarAlgebra B]
  [inst_2 : FunLike F A B] [AlgHomClass F ℂ A B] [StarHomClass F A B] {a : A},
  IsSelfAdjoint a → ∀ (φ : F), Function.Injective ⇑φ → spectrum ℝ (φ a) = spectrum ℝ a

Defined in

Mathlib.Analysis.CStarAlgebra.Hom

Cited by

1 results in Mathlib

Foundations

Depth 311 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CStarAlgebraCStarAlgebraFunLikeAlgHomClassStarHomClass