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Some remarks on smooth renormings of Banach spaces

  1. 1. 0476945 - MU-W 2018 RIV US eng J - Článek v odborném periodiku
    Hájek, Petr Pavel - Russo, T.
    Some remarks on smooth renormings of Banach spaces.
    Journal of Mathematical Analysis and Applications. Roč. 455, č. 2 (2017), s. 1272-1284 ISSN 0022-247X
    Grant CEP: GA ČR GA16-07378S
    Institucionální podpora: RVO:67985840
    Klíčová slova: Fréchet smooth * approximation of norms * Ck-smooth norm
    Kód oboru RIV: BA - Obecná matematika
    Obor OECD: Pure mathematics
    Impakt faktor: 1.138, rok: 2017
    http://www.sciencedirect.com/science/article/pii/S0022247X17305462?via%3Dihub

    We prove that in every separable Banach space X with a Schauder basis and a Ck-smooth norm it is possible to approximate, uniformly on bounded sets, every equivalent norm with a Ck-smooth one in a way that the approximation is improving as fast as we wish on the elements depending only on the tail of the Schauder basis. Our result solves a problem from the recent monograph of Guirao, Montesinos and Zizler.
    Trvalý link: http://hdl.handle.net/11104/0273350
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