Best N-Simultaneous Approximation in Lp(μ, X) . (12th July 2017)

• Record Type: Journal Article
• Authors: Pakhrou, Tijani
• Other Names: Sawano Yoshihiro Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2017(2017)
• Publication Date: 2017-07-12
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2017/7347130
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Let X be a Banach space. Let 1 ≤ p < ∞ and denote by L p ( μ, X ) the Banach space of all X -valued Bochner p -integrable functions on a certain positive complete σ -finite measure space ( Ω, Σ, μ ), endowed with the usual p -norm. In this paper, the theory of lifting is used to prove that, for any weakly compact subset W of X, the set L p ( μ, W ) is N -simultaneously proximinal in L p ( μ, X ) for any arbitrary monotonous norm N in R n .