When is a locally convex space Eberlein-Grothendieck?
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00563646" target="_blank" >RIV/67985840:_____/22:00563646 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00025-022-01770-w" target="_blank" >https://doi.org/10.1007/s00025-022-01770-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-022-01770-w" target="_blank" >10.1007/s00025-022-01770-w</a>
Alternative languages
Result language
angličtina
Original language name
When is a locally convex space Eberlein-Grothendieck?
Original language description
The weak topology of a locally convex space (lcs) E is denoted by w. In this paper we undertake a systematic study of those lcs E such that (E, w) is (linearly) Eberlein-Grothendieck (see Definitions 1.2 and 3.1). The following results obtained in our paper play a key role: for every barrelled lcs E, the space (E, w) is Eberlein-Grothendieck (linearly Eberlein-Grothendieck) if and only if E is metrizable (E is normable, respectively). The main applications concern to the space of continuous real-valued functions on a Tychonoff space X endowed with the compact-open topology Ck(X). We prove that (Ck(X) , w) is Eberlein-Grothendieck (linearly Eberlein-Grothen-dieck) if and only if X is hemicompact (X is compact, respectively). Besides this, we show that the class of E for which (E, w) is linearly Eberlein-Grothendieck preserves linear continuous quotients. Various illustrating examples are provided.
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
Results in Mathematics
ISSN
1422-6383
e-ISSN
1420-9012
Volume of the periodical
77
Issue of the periodical within the volume
6
Country of publishing house
CH - SWITZERLAND
Number of pages
16
Pages from-to
236
UT code for WoS article
000873856800003
EID of the result in the Scopus database
2-s2.0-85140615299