Birkhoff-James orthogonality and applications : A survey

Abstract

In the last few decades, the concept of Birkhoff-James orthogonality has been used in several applications. In this survey article, the results known on the necessary and sufficient conditions for Birkhoff-James orthogonality in certain Banach spaces are mentioned. Their applications in studying the geometry of normed spaces are given. The connections between this concept of orthogonality, and the Gateaux derivative and the subdifferential set of the norm function are provided. Several interesting distance formulas can be obtained using the characterizations of Birkhoff-James orthogonality, which are also mentioned. In the end, some new results are obtained.Comment: To appear in : Springer/Birkh\"auser Verlag book series Operator Theory: Advances and Applications. Number of pages : 1