Number of the records: 1
When is multiplication in a Banach algebra open?
- 1.
SYSNO ASEP 0480794 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title When is multiplication in a Banach algebra open? Author(s) Draga, Szymon (MU-W) SAI, RID
Kania, Tomasz (MU-W) SAI, ORCID, RIDSource Title Linear Algebra and Its Applications. - : Elsevier - ISSN 0024-3795
Roč. 538, 1 February (2018), s. 149-165Number of pages 17 s. Language eng - English Country US - United States Keywords Banach algebra ; open mapping ; uniformly open map Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GF16-34860L GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 UT WOS 000417661200009 EID SCOPUS 85032029175 DOI 10.1016/j.laa.2017.10.007 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2019
Number of the records: 1