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Quantification of Pelczynski's property (V)

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10369898" target="_blank" >RIV/00216208:11320/17:10369898 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1002/mana.201700051" target="_blank" >http://dx.doi.org/10.1002/mana.201700051</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1002/mana.201700051" target="_blank" >10.1002/mana.201700051</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Quantification of Pelczynski's property (V)

  • Original language description

    A Banach space X has Pelczynski&apos;s property (V) if for every Banach space Y every unconditionally converging operator T : X -&gt; Y is weakly compact. In 1962, Aleksander Pelczynski showed that C(K) spaces for a compact Hausdorff space K enjoy the property (V), and some generalizations of this theorem have been proved since then. We introduce several possibilities of quantifying the property (V). We prove some characterizations of the introduced quantitative versions of this property, which allow us to prove a quantitative version of Pelczynski&apos;s result about C(K) spaces and generalize it. Finally, we study the relationship of several properties of operators including weak compactness and unconditional convergence, and using the results obtained we establish a relation between quantitative versions of the property (V) and quantitative versions of other well known properties of Banach spaces.

  • 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/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2017

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Mathematische Nachrichten

  • ISSN

    0025-584X

  • e-ISSN

  • Volume of the periodical

    290

  • Issue of the periodical within the volume

    17-18

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    16

  • Pages from-to

    2909-2924

  • UT code for WoS article

    000419959100017

  • EID of the result in the Scopus database

    2-s2.0-85029223732