Displaying similar documents to “The Krein-Šmulian theorem and its extension”

Measures of noncompactness and normal structure in Banach spaces

J. García-Falset, A. Jiménez-Melado, E. Lloréns-Fuster (1994)

Studia Mathematica

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Sufficient conditions for normal structure of a Banach space are given. One of them implies reflexivity for Banach spaces with an unconditional basis, and also for Banach lattices.

Convex sets in Banach spaces and a problem of Rolewicz

A. Granero, M. Jiménez Sevilla, J. Moreno (1998)

Studia Mathematica

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Let B x be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdorff metric. In the first part of this work we study the density character of B x and investigate its connections with the geometry of the space, in particular with a property shared by the spaces of Shelah and Kunen. In the second part we are concerned with the problem of Rolewicz, namely the existence of support sets, for the case of spaces C(K).