Perturbation of Sets and Centers |
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Authors: | Email author" target="_blank">E?AlvoniEmail author P?L?Papini |
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Institution: | (1) Dipartimento di Matematica, Applicata alle Scienze Economiche e Sociali, Viale Filopanti 5, I-40126 Bologna;(2) Dipartimento di Matematica, Piazza Porta, S. Donato 5, I-40126 Bologna |
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Abstract: | Given a bounded set A, a Chebyshev center (when it exists) is–in some sense–a candidate to give a global information on the
set. Finding the centers of A is of great importance for applications. In many cases, it is very important to understand how
they change when the set A is perturbed. Our main result is a new characterization of Hilbert spaces: in fact, we will show
that the best estimate we can give in these spaces, concerning perturbations of sets, cannot be expected outside this class
of spaces. Moreover, we collect, we partly sharpen and we reprove in a simple way most known results. |
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Keywords: | Center Perturbation of sets Hilbert spaces |
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