Spectral radius formulae

Abstract

If A is a complex Banach algebra (not necessarily unital) and x∈A, σ(x) will denote the spectrum and spectral radius of x in A. If I is a closed two-sided ideal in A let x + I denote the coset in the quotient algebra A/I containing x. Then

Spectral radius formulae in quotient 𝐶*-algebras

“…For x£A denote by r(x) (r(x + I)) the spectral radius of the element x (x + I). G. J. Murphy and T. T. West [ 1, Proposition 4, Corollary] have proved that (1) r…”

Hildebrandt's theorem for the essential spectrum

“…The proof relies on the following lemma by Murphy and West [8]. For the sake of completeness we include its proof.…”

On the perturbation functions and similarity orbits

“…If F · (·) = · e , we obtain the result of [9] in the particular case when the C * -algebra is C(H) = B(H)/K(H). Corollary 2.5.…”