Theorems · Theorem · functional analysis

spectrum_star_mul_self_nonneg

∀ {A : Type u_1} [inst : CStarAlgebra A] {b : A}, ∀ x ∈ spectrum ℝ (star b * b), 0 ≤ x

The ℝ-spectrum of an element of the form star b * b in a C⋆-algebra is nonnegative. This is the key result used to establish CStarAlgebra.instNonnegSpectrumClass.

Defined in

Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic

Cited by

1 results in Mathlib

Foundations

Depth 314 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CStarAlgebra