On linear continuous operators between distinguished spaces Cp(X)
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00546784" target="_blank" >RIV/67985840:_____/21:00546784 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13398-021-01121-4" target="_blank" >https://doi.org/10.1007/s13398-021-01121-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-021-01121-4" target="_blank" >10.1007/s13398-021-01121-4</a>
Alternative languages
Result language
angličtina
Original language name
On linear continuous operators between distinguished spaces Cp(X)
Original language description
As proved in Ka̧kol and Leiderman (Proc AMS Ser B 8:86–99, 2021), for a Tychonoff space X, a locally convex space Cp(X) is distinguished if and only if X is a Δ -space. If there exists a linear continuous surjective mapping T: Cp(X) → Cp(Y) and Cp(X) is distinguished, then Cp(Y) also is distinguished (Ka̧kol and Leiderman Proc AMS Ser B, 2021). Firstly, in this paper we explore the following question: Under which conditions the operator T: Cp(X) → Cp(Y) above is open? Secondly, we devote a special attention to concrete distinguished spaces Cp([1 , α]) , where α is a countable ordinal number. A complete characterization of all Y which admit a linear continuous surjective mapping T: Cp([1 , α]) → Cp(Y) is given. We also observe that for every countable ordinal α all closed linear subspaces of Cp([1 , α]) are distinguished, thereby answering an open question posed in Ka̧kol and Leiderman (Proc AMS Ser B, 2021).
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
2021
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
115
Issue of the periodical within the volume
4
Country of publishing house
ES - SPAIN
Number of pages
11
Pages from-to
199
UT code for WoS article
000698668600001
EID of the result in the Scopus database
2-s2.0-85115337368