Search results

1 – 1 of 1
Per page
102050
Citations:
Loading...
Access Restricted. View access options
Article
Publication date: 2 March 2012

Tijani Pakhrou

In this paper the aim is to present some subspace simultaneously proximinal in the Banach space L1(μ, X) of X‐valued Bochner μ‐integrable functions.

95

Abstract

Purpose

In this paper the aim is to present some subspace simultaneously proximinal in the Banach space L1(μ, X) of X‐valued Bochner μ‐integrable functions.

Design/methodology/approach

By lower semicontinuity and compactness the existence of best simultaneous approximation is obtained.

Findings

If Y is a reflexive subspace of a Banach space X, then L1(μ, Y) is simultaneously proximinal in L1(μ, X). Furthermore, if X is reflexive and μ0 is the restriction of μ to a sub‐σ‐algebra, then L1(μ0, X) is simultaneously proximinal in L1(μ, X).

Practical implications

Given a finite number of points in the Banach space X, is about finding a point in the subspace YX that comes close to all this points.

Originality/value

By the property of reflexivity two types subspaces simultaneously proximinal in L1(μ, X) are obtained.

1 – 1 of 1
Per page
102050