Abstract
It is shown that a Banach spaceX admits an equivalent uniformly Gâteaux smooth norm if and only if the dual ball ofX* in its weak star topology is a uniform Eberlein compact.
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Supported by AV 101-97-02, AV 1019003 and GA ČR 201-98-1449.
Supported by GA ČR 201-98-1449, AV 1019003 and GAUK 1/1998.
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Fabian, M., Godefroy, G. & Zizler, V. The structure of uniformly Gâteaux smooth Banach spaces. Isr. J. Math. 124, 243–252 (2001). https://doi.org/10.1007/BF02772620
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DOI: https://doi.org/10.1007/BF02772620