Počet záznamů: 1

On a classical renorming construction of V. Klee

  1. 1.
    0367447 - MU-W 2012 RIV US eng J - Článek v odborném periodiku
    Guirao, A. J. - Montesinos, V. - Zizler, Václav
    On a classical renorming construction of V. Klee.
    Journal of Mathematical Analysis and Applications. Roč. 385, č. 1 (2012), s. 458-465 ISSN 0022-247X
    Grant CEP: GA AV ČR IAA100190901
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: rotund norm * locally uniformly rotund norm * Gateaux differentiable norm
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 1.050, rok: 2012
    http://www.sciencedirect.com/science/article/pii/S0022247X1100607X

    We further develop a classical geometric construction of V. Klee and show, typically, that if X is a nonreflexive Banach space with separable dual, then X admits an equivalent norm vertical bar . vertical bar which is Frechet differentiable, locally uniformly rotund, its dual norm vertical bar . vertical bar* is uniformly Gateaux differentiable, the weak* and the norm topologies coincide on the sphere of (X*, vertical bar . vertical bar*) and, yet, vertical bar . vertical bar* is not rotund. This proves (a stronger form of) a conjecture of V. Klee.
    Trvalý link: http://hdl.handle.net/11104/0202137
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