Relations between the strong subdifferentiability of a norm and the locally nearly uniformly convex spaces
by
K. Sadarangani
University of Las Palmas de Gran Canaria (SPAIN)
Coauthors: Martinon, A. (University of La Laguna-SPAIN-)

In this paper we investigate some relationships between some concepts of the geometric theory of Banach spaces expressed with the help of compactness conditions and the concept of strong subdifferentiability of a norm.
In particular, we give a characterization of the locally nearly uniformly convex Banach spaces in terms of the strong subdifferentiability of the norm in the dual space.
Moreover, we prove that any separable and reflexive Banach space admits an equivalent nearly strictly convex norm which is not locally nearly uniformly convex.

Date received: February 28, 2001