Paper Title:

Birkhoff-James orthogonality and Best Approximant in L₁(X)

Author(s):

Mecheri Hacene and Rebiai Belgacem

Department of Mathematics and Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
E-mail: mecherih2000@yahoo.fr

Department of Mathematics and Informatics,
LAMIS laboratory, University of Tebessa,
Algeria.
E-mail: brebiai@gmail.com

Abstract:

Let X  be a complex Banach space and let (X,ρ) be a positive measure space. The Birkhoff-James orthogonality is a generalization of Hilbert space orthogonality to Banach spaces. We use this notion of orthogonality to establish a new characterization of Birkhoff-James orthogonality of bounded linear operators in L₁(X,ρ) also implies best approximation has been proved.

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