Subsets of nonempty joint spectrum in topological algebras
Mathematica Bohemica (2018)
- Volume: 143, Issue: 4, page 441-448
- ISSN: 0862-7959
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topWawrzyńczyk, Antoni. "Subsets of nonempty joint spectrum in topological algebras." Mathematica Bohemica 143.4 (2018): 441-448. <http://eudml.org/doc/294836>.
@article{Wawrzyńczyk2018,
abstract = {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)\ne \emptyset $ if and only if $[L,L]$ generates in $\mathcal \{A\}$ a proper left ideal. 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.},
author = {Wawrzyńczyk, Antoni},
journal = {Mathematica Bohemica},
keywords = {joint spectrum; Waelbroeck algebra; commutator; spectral mapping formula},
language = {eng},
number = {4},
pages = {441-448},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Subsets of nonempty joint spectrum in topological algebras},
url = {http://eudml.org/doc/294836},
volume = {143},
year = {2018},
}
TY - JOUR
AU - Wawrzyńczyk, Antoni
TI - Subsets of nonempty joint spectrum in topological algebras
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 4
SP - 441
EP - 448
AB - 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)\ne \emptyset $ if and only if $[L,L]$ generates in $\mathcal {A}$ a proper left ideal. 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.
LA - eng
KW - joint spectrum; Waelbroeck algebra; commutator; spectral mapping formula
UR - http://eudml.org/doc/294836
ER -
References
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- Wawrzyńczyk, A., Joint spectra in Waelbroeck algebras, Bol. Soc. Mat. Mex., III. Ser. 13 (2007), 321-343. (2007) Zbl1178.46047MR2472509
- Wawrzyńczyk, A., 10.4064/ba55-1-7, Bull. Pol. Acad. Sci., Math. 55 (2007), 63-69. (2007) Zbl1118.46045MR2304300DOI10.4064/ba55-1-7
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