Schur Lemma and the Spectral Mapping Formula

• Autorzy: Antoni Wawrzyńczyk
• Języki publikacji: EN

Abstrakty

EN

Let B be a complex topological unital algebra. The left joint spectrum of a set S ⊂ B is defined by the formula
$σ_l(S)$ = {$(λ(s))_{s∈ S} ∈ ℂ^S | {s-λ(s)}_{s∈S}$ generates a proper left ideal}$.
Using the Schur lemma and the Gelfand-Mazur theorem we prove that $σ_l(S)$ has the spectral mapping property for sets S of pairwise commuting elements if
(i) B is an m-convex algebra with all maximal left ideals closed, or
(ii) B is a locally convex Waelbroeck algebra.
The right ideal version of this result is also valid.

Kategorie tematyczne

• 46H10: Ideals and subalgebras
• 46H15: Representations of topological algebras
• 46H30: Functional calculus in topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: 55
• Numer: 1
• Strony: 63-69

Daty

wydano

2007

Twórcy

autor

Antoni Wawrzyńczyk

• Departamento de Matemáticas, Universidad Autónoma Metropolitana - Iztapalapa, Av. San Rafael Atlixco 186, col. Vicentina, AP 55-534, 09 340 México, D.F., Mexico

Identyfikatory

DOI

10.4064/ba55-1-7