Simultaneously proximinality in L_∞(μ, X)

2018/09/21 by Pakhrou, Tijani
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1809.07975

Abstract

It is shown that for any W weakly compact set of a real Banach space X, the set L_∞(μ,W) is N-simultaneously proximinal in L_∞(μ,X) for arbitrary monotonous norm N in ℝⁿ.

Related

• On the sum of simultaneously proximinal sets
• Some remarks on p-median problem
• Approximative compactness in Böchner spaces
• Testing compactness of linear operators
• Best approximation properties in spaces of measurable functions