When is multiplication in a Banach algebra open?

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

When is multiplication in a Banach algebra open?

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

When is multiplication in a Banach algebra open?

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF16-34860L" target="_blank" >GF16-34860L: Logika a topologie v Banachových prostorech</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

—

Svazek periodika

538

Číslo periodika v rámci svazku

1 February

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

149-165

Kód UT WoS článku

000417661200009

EID výsledku v databázi Scopus

2-s2.0-85032029175