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Uniformly Convex Metric Spaces

100%

Kell M.

Analysis and Geometry in Metric Spaces

2014

tom 2

nr 1

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.

Banach-Saks property in some Banach sequence spaces

75%

Cui Y., Hudzik H., Płuciennik R.

Annales Polonici Mathematici

1996-1997

tom 65

nr 2

193-202

It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Annales Polonici Mathematici

1 Cui Y.

1 Hudzik H.

1 Kell M.

1 Płuciennik R.

1 2014

1 1997

Wyniki wyszukiwania

Uniformly Convex Metric Spaces

Banach-Saks property in some Banach sequence spaces