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Networks for the weak topology of Banach and Fréchet spaces
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SYSNO ASEP 0446776 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Networks for the weak topology of Banach and Fréchet spaces Tvůrce(i) Gabriyelyan, S. (IL)
Kąkol, Jerzy (MU-W) SAI, RID, ORCID
Kubiś, Wieslaw (MU-W) RID, ORCID, SAI
Marciszewski, W. (PL)Zdroj.dok. Journal of Mathematical Analysis and Applications. - : Elsevier - ISSN 0022-247X
Roč. 432, č. 2 (2015), s. 1183-1199Poč.str. 17 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova Fréchet space ; space of continuous functions ; locally convex space Vědní obor RIV BA - Obecná matematika CEP GA14-07880S GA ČR - Grantová agentura ČR Institucionální podpora MU-W - RVO:67985840 UT WOS 000360324200037 EID SCOPUS 84939270863 DOI 10.1016/j.jmaa.2015.07.037 Anotace 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 X is 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 and some sufficient conditions on a Fréchet lcs to be an ...-space in the weak topology. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2016
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