A Characterization of Extremal Sets in Hilbert Spaces

TL;DR

This paper characterizes extremal sets in Hilbert spaces, extending classical results, and examines the behavior of points near the circumsphere using measures of non-compactness.

Contribution

It generalizes Jung's theorem to characterize extremal sets in Hilbert spaces and analyzes point behavior near the circumsphere with non-compactness measures.

Findings

Extended Jung's theorem to Hilbert spaces

Analyzed point behavior near the circumsphere

Used Kuratowski and Hausdorff measures of non-compactness

Abstract

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.