Data di Pubblicazione:
2012
Citazione:
Polyhedral direct sums of Banach spaces, and generalized centers of finite sets / L. Vesely. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 391:2(2012), pp. 466-479.
Abstract:
A Banach space $X$ is said to satisfy (GC) if
the set $E_f(a)$ of minimizers
of the function $X\ni x\mapsto f(\|x-a_1\|,\ldots,\|x-a_n\|)$ is nonempty
for each integer $n\ge1$, each $a\in X^n$ 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 $E_f(\cdot)$ on $C(K,X)^n$ ($n\ge1$)
are continuous in the Hausdorff metric for each compact $K$.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Polyhedral Banach space ; Chebyshev center ; generalized centers ; optimal location ; space of continuous functions ; vector-valued function
Elenco autori:
L. Vesely
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