When is multiplication in a Banach algebra open?

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>

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
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

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

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)