J. Aust. Math. Soc.  82 (2007), 429-439

Extremal characterizations of reflexive spaces

Xianfu Wang   Mathematics, The Irving K. Barber School of Arts and Sciences   UBC Okanagan   3333 University Way   Kelowna BC V1V 1V7   Canada   Shawn.Wang@ubc.ca

Abstract

Assume that a Banach space has a Fréchet differentiable and locally uniformly convex norm. We show that the reflexive property of the Banach space is not only sufficient, but also a necessary condition for the fulfillment of the proximal extremal principle in nonsmooth analysis.

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