Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/592

 Title: Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms Authors: Fabian, MariánHájek, PetrZizler, Václav Keywords: Uniform Eberlein CompactaUniform Gâteaux Smooth NormsWeak Compact Generating Issue Date: 1997 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 23, No 3-4, (1997), 351p-362p Abstract: It is shown that the dual unit ball BX∗ of a Banach space X∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a uniformly Gâteaux smooth norm and X is a subspace of a weakly compactly generated space. The bidual unit ball BX∗∗ of a Banach space X∗∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a weakly uniformly rotund norm. In this case X admits a locally uniformly rotund and Fréchet differentiable norm. An Eberlein compact K is a uniform Eberlein compact if and only if C(K) admits a uniformly Gˆateaux differentiable norm. Description: * Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada). URI: http://hdl.handle.net/10525/592 ISSN: 1310-6600 Appears in Collections: Volume 23 Number 3-4

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