A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space |
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Authors: | Marián Fabian Stanimir Troyanski |
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Affiliation: | 1. Sibeliova 49, 162 00, Prague 6, Czechoslovakia 2. Department of Mathematics and Informatics, University of Sofia, 5, Boullevard A. Ivanou, 1126, Sofia, Bulgaria
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Abstract: | LetV be a Banach space whose dualV * is Va?ák, that is, weakly countably determined. Then an equivalent locally uniformly rotund norm onV is constructed. According to a recent example of Mercourakis, this is a real extension of an earlier result of Godefroy Troyanski, Whitfield and Zizler, whereV * has been a subspace of a weakly compactly generated Banach space. |
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