Polyhedral direct sums of Banach spaces, and generalized centers of finite sets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:391

Article

Vesely, Libor

关键词: Polyhedral Banach space;    Chebyshev center;    Generalized centers;    Optimal location;    Space of continuous functions;    Vector-valued function;   

DOI  :  10.1016/j.jmaa.2012.02.048

来源: Elsevier

【 摘 要 】

A Banach space X is said to satisfy (GC) if the set E-f(a) of minimizers of the function X (sic) x (sic) f(parallel to x - a(1)parallel to, ... , parallel to x - a(n)parallel to) is nonempty for each integer n >= 1, each a is an element of X-n and each continuous nondecreasing coercive real-valued function f on R-+(n) We study stability of certain polyhedrality properties under making direct sums, in order to be able to use results from a paper by Fonf, Lindenstrauss and the author to show that if X satisfies (GC) and an appropriate polyhedrality property then the function space C-b(T, X) satisfies (GC) for every topological space T. This generalizes the author's result from 1997, proved for finite-dimensional polyhedral spaces X. Moreover, under more restrictive conditions on X and f, the mappings E-f(.) on C(K, X)(n) (n >= 1) are continuous in the Hausdorff metric for each compact K. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free