On proximinality of convex sets in superspaces

Authors

Li Xin Cheng, Xiamen University
Zheng Hua Luo, Huaqiao University
Wen Zhang, Xiamen UniversityFollow
Ben Tuo Zheng, University of MemphisFollow

Abstract

In this paper, we show that a closed convex subset C of a Banach space is strongly proximinal (proximinal, resp.) in every Banach space isometrically containing it if and only if C is locally (weakly, resp.) compact. As a consequence, it is proved that local compactness of C is also equivalent to that for every Banach space Y isometrically containing it, the metric projection from Y to C is nonempty set-valued and upper semi-continuous.

Publication Title

Acta Mathematica Sinica, English Series

Recommended Citation

Cheng, L., Luo, Z., Zhang, W., & Zheng, B. (2016). On proximinality of convex sets in superspaces. Acta Mathematica Sinica, English Series, 32 (6), 633-642. https://doi.org/10.1007/s10114-016-5355-0