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Preserved extreme points. (English. Russian original) Zbl 0591.46004
Funct. Anal. Appl. 19, 144-146 (1985); translation from Funkts. Anal. Prilozh. 19, No. 2, 76-77 (1985).
An extreme point of the unit ball in a Banach space X is said to be preserved if its image under the canonical mapping from X into its second dual $$X^{**}$$ is an extreme point of the unit ball in $$X^{**}$$. The author proves that X is reflexive if and only if every extreme point of its unit ball is preserved in each equivalent norm.
Reviewer: C.M.Edwards
##### MSC:
 46A55 Convex sets in topological linear spaces; Choquet theory 46B10 Duality and reflexivity in normed linear and Banach spaces
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##### References:
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