Theorems · Theorem · functional analysis

NonnegSpectrumClass.quasispectrum_nonneg_of_nonneg

∀ {𝕜 : Type u_3} {A : Type u_4} {inst : CommSemiring 𝕜} {inst_1 : PartialOrder 𝕜} {inst_2 : NonUnitalRing A}
  {inst_3 : PartialOrder A} {inst_4 : Module 𝕜 A} [self : NonnegSpectrumClass 𝕜 A] (a : A),
  0 ≤ a → ∀ x ∈ quasispectrum 𝕜 a, 0 ≤ x

Defined in

Mathlib.Algebra.Algebra.Spectrum.Quasispectrum

Cited by

9 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonnegSpectrumClass