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When is multiplication in a Banach algebra open?

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, RID}
Source Title	Linear Algebra and Its Applications. - : Elsevier - ISSN 0024-3795 Roč. 538, 1 February (2018), s. 149-165
Number 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