Weak near convexity and smoothness of Banach spaces. (English) Zbl 1021.46012

The aim of this paper is to use the De Blasi measure of weak noncompactness instead of the Hausdorff measure of noncompactness – which allows introduction of a class of Banach spaces wider than the class of the nearly smooth Banach spaces. It is proven that the weak near smoothness (studied here) is a property transmitted to closed subspaces. These properties are also illustrated for some classic Banach spaces.


46B20 Geometry and structure of normed linear spaces
46B25 Classical Banach spaces in the general theory
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