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Flat sets, l(p)-generating and fixing c(0) in the nonseparable setting

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    0336577 - MÚ 2010 RIV AU eng J - Journal Article
    Fabian, Marián - Gonzáles, A. - Zizler, Václav
    Flat sets, l(p)-generating and fixing c(0) in the nonseparable setting.
    [Ploché množiny, l(p)-generování a usazení c(0) v neseparabilním případě.]
    Journal of the Australian Mathematical Society Series A-Pure Mathematics and Statistics. Roč. 87, č. 2 (2009), s. 197-210. ISSN 1446-7887. E-ISSN 1446-8107
    R&D Projects: GA AV ČR(CZ) IAA100190610; GA ČR GA201/07/0394
    Institutional research plan: CEZ:AV0Z10190503
    Keywords : Lipschitz-weak*-Kadets-Klee norm * c(0)(Gamma)-generated space * l(p)(Gamma)-generated space * weakly compactly generated space * asymptotically p-flat set * innerly asymptotically p-flat set
    Subject RIV: BA - General Mathematics
    Impact factor: 0.348, year: 2009

    In terms of uniform weak* Kadec-Klee asymptotic smoothnes, and use these concepts to characterize weakly compactly generated (Asplund) spaces that are c(0)(omega(1))-generated or l(p)(omega(1))-generated, where p is an element of (1, infinity) In particular, we show that every subspace of c(0)(omega(1)) is c(0)(omega(1))-generated and every subspce of l(p)(omega(1)) is l(p)(omega(1))-generated for every p is an element of (1, infinity). As a byproduct of the technology of projectional resolutions of the identity we get an alternative proof of Rosenthal's theorem on fixing c(0)(omega(1)).

    V řeči unoformní slabé* Kadecovy-Kleeovy asymptotické hladkosti definujeme asymptoticky p-ploché a vnitřně asymptoticky p-ploché množiny v Banachových prostorech. Pak užíváme tyto pojmy k charakterizaci WCG (asplundovských) prostorů, které jsou c(0)(omega(1))- generovány anebo l(p)(omega(1)) - generovány, kde l<p<nekonečno. Obvzláště dostaneme, že každý prostor l(p)(omega(1)) je c(0)(omega(1)) je c(0)(omega(1))- generovaný a každý podprostor l(p)(omega(1)) je l(p)(omega(1)) - generovaný pro každé lp<nekonečno. Jako vedlejší produkt techniky používání PRI dostáváme alternativní důkaz Rosenthalovy věty o usazení c(0)(omega(1)).
    Permanent Link: http://hdl.handle.net/11104/0180781

     
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