Unital Banach algebras not isomorphic to Calkin algebras of separable Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00545833" target="_blank" >RIV/67985840:_____/21:00545833 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/proc/15589" target="_blank" >https://doi.org/10.1090/proc/15589</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/15589" target="_blank" >10.1090/proc/15589</a>

Result language
angličtina
Original language name
Unital Banach algebras not isomorphic to Calkin algebras of separable Banach spaces
Original language description
Recent developments in Banach space theory provided unexpected examples of unital Banach algebras that are isomorphic to Calkin algebras of Banach spaces, however no example of a unital Banach algebra that cannot be realised as a Calkin algebra has been found so far. This naturally led to the question of possible limitations of such assignments. In the present note we provide examples of unital Banach algebras meeting the necessary density condition for being the Calkin algebra of a separable Banach space that are not isomorphic to Calkin algebras of such spaces, nonetheless. The examples may be found of the form C(X) for a compact space X, ℓ1(G) for some torsion-free Abelian group, and a simple, unital AF C∗-algebra. Extensions to higher densities are also presented.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ19-07129Y" target="_blank" >GJ19-07129Y: Linear-analysis techniques in operator algebras and vice versa</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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