Schur Lemma and the Spectral Mapping Formula

Antoni Wawrzyńczyk. "Schur Lemma and the Spectral Mapping Formula." Bulletin of the Polish Academy of Sciences. Mathematics 55.1 (2007): 63-69. <http://eudml.org/doc/280516>.

@article{AntoniWawrzyńczyk2007,
abstract = {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.},
author = {Antoni Wawrzyńczyk},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Waelbroeck algebra; joint spectrum; spectral mapping formula},
language = {eng},
number = {1},
pages = {63-69},
title = {Schur Lemma and the Spectral Mapping Formula},
url = {http://eudml.org/doc/280516},
volume = {55},
year = {2007},
}

TY - JOUR
AU - Antoni Wawrzyńczyk
TI - Schur Lemma and the Spectral Mapping Formula
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2007
VL - 55
IS - 1
SP - 63
EP - 69
AB - 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.
LA - eng
KW - Waelbroeck algebra; joint spectrum; spectral mapping formula
UR - http://eudml.org/doc/280516
ER -