Schur Lemma and the Spectral Mapping Formula

Antoni Wawrzyńczyk

Bulletin of the Polish Academy of Sciences. Mathematics (2007)

  • Volume: 55, Issue: 1, page 63-69
  • ISSN: 0239-7269

Abstract

top
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 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.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.