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When is multiplication in a Banach algebra open?
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SYSNO ASEP 0480794 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název When is multiplication in a Banach algebra open? Tvůrce(i) Draga, Szymon (MU-W) SAI, RID
Kania, Tomasz (MU-W) SAI, ORCID, RIDZdroj.dok. Linear Algebra and Its Applications. - : Elsevier - ISSN 0024-3795
Roč. 538, 1 February (2018), s. 149-165Poč.str. 17 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova Banach algebra ; open mapping ; uniformly open map Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GF16-34860L GA ČR - Grantová agentura ČR Institucionální podpora MU-W - RVO:67985840 UT WOS 000417661200009 EID SCOPUS 85032029175 DOI 10.1016/j.laa.2017.10.007 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2019
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