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Stable smooth and extreme points, and reflexivity. (English) Zbl 0816.46010

Summary: The property “for any equivalent norm each extreme point of the unit ball is an extreme point of the second dual unit ball” characterizes reflexive Banach spaces. If we consider smooth points instead of extreme points, the corresponding property characterizes Grothendieck spaces. Some other characterizations of reflexivity in terms of renormings are given for WCG Banach spaces.

MSC:

46B20 Geometry and structure of normed linear spaces
46B10 Duality and reflexivity in normed linear and Banach spaces
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