---
abstract: 'In this paper, we study Birkhoff-James orthogonality of bounded linear operators and give a complete characterization of Birkhoff-James orthogonality of bounded linear operators on infinite dimensional real normed linear spaces. As an application of the results obtained, we prove a simple but useful characterization of Birkhoff-James orthogonality of bounded linear functionals defined on a real normed linear space, provided the dual space is strictly convex. We also provide separate necessary and sufficient conditions for smoothness of bounded linear operators on infinite dimensional normed linear spaces.'
address:
- |
    Department of Mathematics\
    Indian Institute of Science\
    Bengaluru 560012\
    Karnataka\
    India\
- |
    Department of Mathematics\
    Jadavpur University\
    Kolkata 700032\
    West Bengal\
    INDIA
- |
    Department of Mathematics\
    Jadavpur University\
    Kolkata 700032\
    West Bengal\
    INDIA
author:
- 'Debmalya Sain, Kallol Paul and Arpita Mal'
title: ' A complete characterization of Birkhoff-James orthogonality in infinite dimensional normed space'
---

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Introduction.
=============

Birkhoff-James orthogonality [@B; @Ja] of elements in a normed linear space was introduced by Birkhoff in [@B], in order to generalize the concept of orthogonality in inner product spaces. Over the years, Birkhoff-James orthogonality has been undoubtedly established as an important concept in the study of geometry of normed 