Continuity of coordinate functionals of filter bases in Banach spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00569855" target="_blank" >RIV/67985840:_____/23:00569855 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2023.109869" target="_blank" >https://doi.org/10.1016/j.jfa.2023.109869</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2023.109869" target="_blank" >10.1016/j.jfa.2023.109869</a>
Alternative languages
Result language
angličtina
Original language name
Continuity of coordinate functionals of filter bases in Banach spaces
Original language description
We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long as the underlying filter is analytic. This removes the large-cardinal hypothesis from the result established by the two last-named authors (Kania and Swaczyna, 2021 [9]) at the expense of reducing the generality from projective to analytic. In particular, we obtain a ZFC solution to Kadets' problem of continuity of coordinate functionals associated with bases with respect to the filter of statistical convergence. Even though the automatic continuity of coordinate functionals beyond the projective class remains a mystery, we prove that a basis with respect to an arbitrary filter that has continuous coordinate functionals is also a basis with respect to a filter that is analytic.
Czech name
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Czech description
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Classification
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
Result continuities
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
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Functional Analysis
ISSN
0022-1236
e-ISSN
1096-0783
Volume of the periodical
284
Issue of the periodical within the volume
9
Country of publishing house
US - UNITED STATES
Number of pages
9
Pages from-to
109869
UT code for WoS article
000944346100001
EID of the result in the Scopus database
2-s2.0-85148346532