Theorems · Theorem · functional analysis

ContinuousFunctionalCalculus.spectrum_nonempty

∀ {R : Type u_1} {A : Type u_2} {p : outParam (A → Prop)} {inst : CommSemiring R} {inst_1 : StarRing R}
  {inst_2 : MetricSpace R} {inst_3 : IsTopologicalSemiring R} {inst_4 : ContinuousStar R} {inst_5 : Ring A}
  {inst_6 : StarRing A} {inst_7 : TopologicalSpace A} {inst_8 : Algebra R A} [self : ContinuousFunctionalCalculus R A p]
  [Nontrivial A] (a : A), p a → (spectrum R a).Nonempty

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital

Cited by

6 results in Mathlib

Foundations

Depth 18 from the axioms · uses no axioms

Assumes

ContinuousFunctionalCalculusNontrivial