1. Polyhedral direct sums of Banach spaces, and generalized centers of finite sets
- Author
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Veselý, Libor
- Subjects
- *
BANACH spaces , *GENERALIZATION , *SET theory , *DIMENSIONAL analysis , *PROOF theory , *MATHEMATICAL mappings - Abstract
Abstract: A Banach space X is said to satisfy if the set of minimizers of the function is nonempty for each integer , each and each continuous nondecreasing coercive real-valued function f on . 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 and an appropriate polyhedrality property then the function space satisfies for every topological space T. This generalizes the authorʼs result from 1997, proved for finite-dimensional polyhedral spaces X. Moreover, under more restrictive conditions on X and f, the mappings on () are continuous in the Hausdorff metric for each compact K. [Copyright &y& Elsevier]
- Published
- 2012
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