Some examples concerning proximinality in Banach spaces

Zihou Zhang ^[1] ; Chunyan Liu ^[1] ; Yu Zhou ^[1]
1. [1] Shanghai University of Engineering Science, PR China
Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 200, Nº 1 (December 2015), 2015, págs. 136-143
Idioma: inglés
DOI: 10.1016/j.jat.2015.06.002
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Resumen
- We discuss the relationships between τ-strongly Chebyshev, τ-approximative compactness, τ-strong proximinality, and proximinality, where τ stands for the norm topology or weak topology. We consider four examples which illustrate the differences, and a counterexample that shows the question regarding the approximative n-compact Chebyshev subset, raised by Bandyopadhyay et al., is negative.