Convex sets in Banach spaces and a problem of Rolewicz

A. Granero; M. Jiménez Sevilla; J. Moreno

Studia Mathematica (1998)

  • Volume: 129, Issue: 1, page 19-29
  • ISSN: 0039-3223

Abstract

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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).

How to cite

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Granero, A., Jiménez Sevilla, M., and Moreno, J.. "Convex sets in Banach spaces and a problem of Rolewicz." Studia Mathematica 129.1 (1998): 19-29. <http://eudml.org/doc/216488>.

@article{Granero1998,
abstract = {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).},
author = {Granero, A., Jiménez Sevilla, M., Moreno, J.},
journal = {Studia Mathematica},
keywords = {Hausdorff metric; density character; existence of support sets},
language = {eng},
number = {1},
pages = {19-29},
title = {Convex sets in Banach spaces and a problem of Rolewicz},
url = {http://eudml.org/doc/216488},
volume = {129},
year = {1998},
}

TY - JOUR
AU - Granero, A.
AU - Jiménez Sevilla, M.
AU - Moreno, J.
TI - Convex sets in Banach spaces and a problem of Rolewicz
JO - Studia Mathematica
PY - 1998
VL - 129
IS - 1
SP - 19
EP - 29
AB - 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).
LA - eng
KW - Hausdorff metric; density character; existence of support sets
UR - http://eudml.org/doc/216488
ER -

References

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