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Title: Subsets of nonempty joint spectrum in topological algebras (English)
Author: Wawrzyńczyk, Antoni
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 143
Issue: 4
Year: 2018
Pages: 441-448
Summary lang: English
Category: math
Summary: We give a necessary and a sufficient condition for a subset $S$ of a locally convex Waelbroeck algebra $\mathcal A$ to have a non-void left joint spectrum $\sigma _l(S).$ In particular, for a Lie subalgebra $L\subset \mathcal A$ we have $\sigma _l(L)\neq \emptyset $ if and only if $[L,L]$ generates in $\mathcal A$ a proper left ideal. \endgraf We also obtain a version of the spectral mapping formula for a modified left joint spectrum. Analogous theorems for the right joint spectrum and the Harte spectrum are also valid. (English)
Keyword: joint spectrum
Keyword: Waelbroeck algebra
Keyword: commutator
Keyword: spectral mapping formula
MSC: 46H30
MSC: 47A13
MSC: 47A60
idZBL: Zbl 06997377
idMR: MR3895267
DOI: 10.21136/MB.2018.0098-17
Date available: 2018-11-29T09:26:33Z
Last updated: 2020-07-01
Stable URL:
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Reference: [4] Nuñez, J. R.: A Joint Spectrum Associated to an Ideal.Tesis de Maestría, Universidad Autónoma Metropolitana, Ciudad de México (2017).
Reference: [5] Pryde, A. J., So{ł}tysiak, A.: On joint spectra of non-commuting normal operators.Bull. Aust. Math. Soc. 48 (1993), 163-170. Zbl 0810.47003, MR 1227446, 10.1017/S0004972700015562
Reference: [6] Wawrzyńczyk, A.: Joint spectra in Waelbroeck algebras.Bol. Soc. Mat. Mex., III. Ser. 13 (2007), 321-343. Zbl 1178.46047, MR 2472509
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