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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 10, 2014

Uniformly Convex Metric Spaces

  • Martin Kell EMAIL logo

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.

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Received: 2014-07-07
Accepted: 2014-11-14
Published Online: 2014-12-10
Published in Print: 2014-01-01

© 2014 Martin Kell

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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