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A note about certain geometric properties of the norm of a dual Banach space. (English) Zbl 0623.46009
The following renorming theorem for a Banach space E is proved: if E is weakly compactly generated, then E can be equivalently renormed in such a way that \(E^*\) is weak* locally uniformly convex. Some consequences of this result are proved. [For related results see G. Godefroy, S. Troyanski, J. H. M. Whitfield and V. Zizler, J. Funct. Anal. 52, 344-352 (1983; Zbl 0517.46010)].
Reviewer: P.L.Papini
46B20 Geometry and structure of normed linear spaces
46B10 Duality and reflexivity in normed linear and Banach spaces
46B03 Isomorphic theory (including renorming) of Banach spaces