Networks for the weak topology of Banach and Fréchet spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00446776" target="_blank" >RIV/67985840:_____/15:00446776 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2015.07.037" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2015.07.037</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2015.07.037" target="_blank" >10.1016/j.jmaa.2015.07.037</a>
Alternative languages
Result language
angličtina
Original language name
Networks for the weak topology of Banach and Fréchet spaces
Original language description
We start the systematic study of Fréchet spaces which are ...-spaces in the weak topology. A topological space X is an ...-space or an ...-space if X has a countable k-network or a sigma-locally finite k -network, respectively. We are motivated by the following result of Corson (1966): If the space Cc(X)Cc(X) of continuous real-valued functions on a Tychonoff space X endowed with the compact-open topology is a Banach space, then Cc(X)Cc(X) endowed with the weak topology is an ...-space if and only if Xis countable. We extend Corson's result as follows: If the space ... is a Fréchet lcs, then E endowed with its weak topology sigma(E,E)sigma(E,E) is an ...-space if and only if ... is an ...-space if and only if X is countable. We obtain a necessary andsome sufficient conditions on a Fréchet lcs to be an ...-space in the weak topology.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA14-07880S" target="_blank" >GA14-07880S: Methods of function theory and Banach algebras in operator theory V.</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
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Volume of the periodical
432
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
1183-1199
UT code for WoS article
000360324200037
EID of the result in the Scopus database
2-s2.0-84939270863