Schur Lemma and the Spectral Mapping Formula
Antoni Wawrzyńczyk
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007), p. 63-69 / Harvested from The Polish Digital Mathematics Library
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Let B be a complex topological unital algebra. The left joint spectrum of a set S ⊂ B is defined by the formula σl(S) = (λ(s))s∈S∈ℂS|s-λ(s)s∈S generates a proper left ideal.Using the Schur lemma and the Gelfand-Mazur theorem we prove that σl(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.

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:280516 
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     volume = {55},
     year = {2007},
     pages = {63-69},
     zbl = {1118.46045},
     language = {en},
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Antoni Wawrzyńczyk. Schur Lemma and the Spectral Mapping Formula. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 63-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-7/