Feral dual spaces and (strongly) distinguished spaces C(X)
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00571369" target="_blank" >RIV/67985840:_____/23:00571369 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13398-023-01417-7" target="_blank" >https://doi.org/10.1007/s13398-023-01417-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-023-01417-7" target="_blank" >10.1007/s13398-023-01417-7</a>
Alternative languages
Result language
angličtina
Original language name
Feral dual spaces and (strongly) distinguished spaces C(X)
Original language description
Following Dieudonné and Schwartz a locally convex space is distinguished if its strong dual is barrelled. The distinguished property for spaces Cp(X) of continuous real-valued functions over a Tychonoff space X is a peculiar (although applicable) property. It is known that Cp(X) is distinguished if and only if Cp(X) is large in RX if and only if X is a Δ -space (in sense of Reed) if and only if the strong dual of Cp(X) carries the finest locally convex topology. Our main results about spaces whose strong dual has only finite-dimensional bounded sets (see Theorems 2, 7 and Proposition 4) are used to study distinguished spaces Ck(X) with the compact-open topology. We also put together several known facts (Theorem 6) about distinguished spaces Cp(X) with self-contained full proofs.
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/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</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
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales
ISSN
1578-7303
e-ISSN
1579-1505
Volume of the periodical
117
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
15
Pages from-to
94
UT code for WoS article
000963878200001
EID of the result in the Scopus database
2-s2.0-85152537442