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On a classical renorming construction of V. Klee
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SYSNO ASEP 0367447 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On a classical renorming construction of V. Klee Author(s) Guirao, A. J. (ES)
Montesinos, V. (ES)
Zizler, Václav (MU-W) RID, SAISource Title Journal of Mathematical Analysis and Applications. - : Elsevier - ISSN 0022-247X
Roč. 385, č. 1 (2012), s. 458-465Number of pages 8 s. Language eng - English Country US - United States Keywords rotund norm ; locally uniformly rotund norm ; Gateaux differentiable norm Subject RIV BA - General Mathematics R&D Projects IAA100190901 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000294979100044 EID SCOPUS 80051793688 DOI 10.1016/j.jmaa.2011.06.059 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2012
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