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When is multiplication in a Banach algebra open?

The result's identifiers

  • 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>

Alternative languages

  • 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

Classification

  • 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

Result continuities

  • 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

Others

  • Publication year

    2018

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Linear Algebra and Its Applications

  • ISSN

    0024-3795

  • e-ISSN

  • Volume of the periodical

    538

  • Issue of the periodical within the volume

    1 February

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    17

  • Pages from-to

    149-165

  • UT code for WoS article

    000417661200009

  • EID of the result in the Scopus database

    2-s2.0-85032029175