Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00539372" target="_blank" >RIV/67985840:_____/21:00539372 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1112/blms.12415" target="_blank" >https://doi.org/10.1112/blms.12415</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/blms.12415" target="_blank" >10.1112/blms.12415</a>

Result language
angličtina
Original language name
Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces
Original language description
Assuming the existence of certain large cardinal numbers, we prove that for every projective filter (Formula presented.) over the set of natural numbers, (Formula presented.) -bases in Banach spaces have continuous coordinate functionals. In particular, this applies to the filter of statistical convergence, thereby we solve a problem by Kadets (at least under the presence of certain large cardinals). In this setting, we recover also a result of Kochanek (Studia Math., 2012) who proved continuity of coordinate functionals for countably generated filters.
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
—
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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