Topologies related to (I)-envelopes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509879" target="_blank" >RIV/00216208:11320/25:10509879 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=P2GwoFgDO9" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=P2GwoFgDO9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2024.109103" target="_blank" >10.1016/j.topol.2024.109103</a>

Result language
angličtina
Original language name
Topologies related to (I)-envelopes
Original language description
We investigate the question whether the (I)-envelope of any subset of a dual to a Banach space X may be described as the closed convex hull in a suitable topology. If X contains no copy of B1 then the weak topology generated by functionals of the first Baire class in the weak & lowast; topology works. On the other hand, if X contains a complemented copy of B1 or X = C([0, 1]) no locally convex topology works. If we do not require the topology to be locally convex, the problem is still open. We further introduce and compare several natural intermediate closure operators on a dual Banach space. Finally, we collect several intriguing open problems related to (I)-envelopes.
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/GA23-04776S" target="_blank" >GA23-04776S: Interplay of algebraic, metric, geometric and topological structures on Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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