Uniformly Convex Metric Spaces

• Autorzy: Martin Kell
• Języki publikacji: EN

Abstrakty

EN

In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology, called coconvex topology, agrees with the usually weak topology in Banach spaces. An example of a CAT(0)-space with weak topology which is not Hausdorff is given. In the end existence and uniqueness of generalized barycenters is shown, an application to isometric group actions is given and a Banach-Saks property is proved.

Słowa kluczowe

EN

convex metric spaces; weak topologies; generalized barycenters; Banach-Saks property

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-07-07

zaakceptowano

2014-11-14

online

2014-12-10

Twórcy

autor

Martin Kell

• Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany

Bibliografia

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Identyfikatory

DOI

10.2478/agms-2014-0015