# Uniformly Convex Metric Spaces

Analysis and Geometry in Metric Spaces (2014)

- Volume: 2, Issue: 1, page 359-380, electronic only
- ISSN: 2299-3274

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topMartin Kell. "Uniformly Convex Metric Spaces." Analysis and Geometry in Metric Spaces 2.1 (2014): 359-380, electronic only. <http://eudml.org/doc/268793>.

@article{MartinKell2014,

abstract = {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.},

author = {Martin Kell},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {convex metric spaces; weak topologies; generalized barycenters; Banach-Saks property; ; convex metric space; Busemann curvature; convex subset; reflexivity; weak topology; barycenter; generalized convexity},

language = {eng},

number = {1},

pages = {359-380, electronic only},

title = {Uniformly Convex Metric Spaces},

url = {http://eudml.org/doc/268793},

volume = {2},

year = {2014},

}

TY - JOUR

AU - Martin Kell

TI - Uniformly Convex Metric Spaces

JO - Analysis and Geometry in Metric Spaces

PY - 2014

VL - 2

IS - 1

SP - 359

EP - 380, electronic only

AB - 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.

LA - eng

KW - convex metric spaces; weak topologies; generalized barycenters; Banach-Saks property; ; convex metric space; Busemann curvature; convex subset; reflexivity; weak topology; barycenter; generalized convexity

UR - http://eudml.org/doc/268793

ER -

## References

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