A note on Banach spaces E for which Ew is homeomorphic to Cp(X)
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00559489" target="_blank" >RIV/67985840:_____/22:00559489 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13398-022-01292-8" target="_blank" >https://doi.org/10.1007/s13398-022-01292-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-022-01292-8" target="_blank" >10.1007/s13398-022-01292-8</a>
Alternative languages
Result language
angličtina
Original language name
A note on Banach spaces E for which Ew is homeomorphic to Cp(X)
Original language description
Cp(X) denotes the space of continuous real-valued functions on a Tychonoff space X endowed with the topology of pointwise convergence. A Banach space E equipped with the weak topology is denoted by Ew. It is unknown whether Cp(K) and C(L) w can be homeomorphic for infinite compact spaces K and L (Krupski, Rev R Acad Cienc Exact Fis Nat Ser A Mat (RACSAM) 110:557–563, 2016, Krupski and Marciszewski, J Math Anal Appl 452:646–658, 2017). In this paper we deal with a more general question: does there exist a Banach space E such that Ew is homeomorphic to the space Cp(X) for some infinite Tychonoff space X? We show that if such homeomorphism exists, then (a) X is a countable union of compact sets Xn, n∈ ω, where at least one component Xn is non-scattered, (b) the Banach space E necessarily contains an isomorphic copy of the Banach space ℓ1.
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
2022
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
116
Issue of the periodical within the volume
4
Country of publishing house
ES - SPAIN
Number of pages
8
Pages from-to
150
UT code for WoS article
000824675900001
EID of the result in the Scopus database
2-s2.0-85134541846