2022/02/09 by Teena Thomas, Thomas, Teena
Mathematics · Computer Science · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2202.04292
In this paper, we provide a necessary and sufficient condition for the existence of a restricted Chebyshev center of a compact subset of an L1-predual space in a closed convex subset of the L1-predual space. We also provide a geometrical characterization of an L1-predual space in terms of the restricted Chebyshev radius in the following manner. A real Banach space X is an L1-predual space if and only if for each non-empty finite subset F of X and closed convex subset V of X, radV(F) = radX(F) + d(V, centX(F)), where we denote radX(F), radV(F), centX(F) and d(V, centX(F)) to be the Chebyshev radius of F in X, the restricted Chebyshev radius of F in V, the set of Chebyshev centers of F in X and the distance between the sets V and centX(F) respectively. Furthermore, we explicitly describe the Chebyshev centers of closed bounded subsets of an M-summand in the space of real-valued continuous functions on a compact Hausdorff space.