When is multiplication in a Banach algebra open?
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00480794" target="_blank" >RIV/67985840:_____/18:00480794 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.laa.2017.10.007" target="_blank" >http://dx.doi.org/10.1016/j.laa.2017.10.007</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2017.10.007" target="_blank" >10.1016/j.laa.2017.10.007</a>
Alternative languages
Result language
angličtina
Original language name
When is multiplication in a Banach algebra open?
Original language description
We develop the theory of Banach algebras whose multiplication (regarded as a bilinear map) is open. We demonstrate that such algebras must have topological stable rank 1, however the latter condition is strictly weaker and implies only that products of non-empty open sets have non-empty interior. We then investigate openness of convolution in semigroup algebras resolving in the negative a problem of whether convolution in ...1(N0) is open. By appealing to ultraproduct techniques, we demonstrate that neither in ...1(Z) nor in ...1(Q) convolution is uniformly open. The problem of openness of multiplication in Banach algebras of bounded operators on Banach spaces and their Calkin algebras is also discussed.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GF16-34860L" target="_blank" >GF16-34860L: Logic and Topology in Banach spaces</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
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Volume of the periodical
538
Issue of the periodical within the volume
1 February
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
149-165
UT code for WoS article
000417661200009
EID of the result in the Scopus database
2-s2.0-85032029175