A Characterization of Extremal Sets in Hilbert Spaces
We give a characterization of extremal sets in Hilbert spaces that generalizes a classical theorem of H. W. E. Jung. We investigate also the behaviour of points near to the circumsphere of such a set with respect to the Kuratowski and Hausdorff measures of non-compactness.
Perturbation of Sets and Centers
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.
A class of spaces lacking normal structure
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