omega(omega)-base and infinite-dimensional compact sets in locally convex spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00557877" target="_blank" >RIV/67985840:_____/22:00557877 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13163-021-00397-9" target="_blank" >https://doi.org/10.1007/s13163-021-00397-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13163-021-00397-9" target="_blank" >10.1007/s13163-021-00397-9</a>
Alternative languages
Result language
angličtina
Original language name
omega(omega)-base and infinite-dimensional compact sets in locally convex spaces
Original language description
A locally convex space (lcs) E is said to have an ωω-base if E has a neighborhood base { Uα: α∈ ωω} at zero such that Uβ⊆ Uα for all α≤ β. The class of lcs with an ωω-base is large, among others contains all (LM)-spaces (hence (LF)-spaces), strong duals of distinguished Fréchet lcs (hence spaces of distributions D′(Ω)). A remarkable result of Cascales-Orihuela states that every compact set in an lcs with an ωω-base is metrizable. Our main result shows that every uncountable-dimensional lcs with an ωω-base contains an infinite-dimensional metrizable compact subset. On the other hand, the countable-dimensional vector space φ endowed with the finest locally convex topology has an ωω-base but contains no infinite-dimensional compact subsets. It turns out that φ is a unique infinite-dimensional locally convex space which is a kR-space containing no infinite-dimensional compact subsets. Applications to spaces Cp(X) are provided.
Czech name
—
Czech description
—
Classification
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
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 Mathématica Complutense
ISSN
1139-1138
e-ISSN
1988-2807
Volume of the periodical
35
Issue of the periodical within the volume
2
Country of publishing house
ES - SPAIN
Number of pages
16
Pages from-to
599-614
UT code for WoS article
000652075100001
EID of the result in the Scopus database
2-s2.0-85106217998