Affiliation:
1. Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany
Abstract
Abstract
In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit ageneralized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simpleproof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology, called coconvextopology, agrees with the usually weak topology in Banach spaces. An example of a CAT(0)-spacewith weak topology which is not Hausdorff is given.In the end existence and uniqueness of generalized barycenters is shown, an application to isometric groupactions is given and a Banach-Saks property is proved.
Subject
Applied Mathematics,Geometry and Topology,Analysis
Cited by
11 articles.
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