A complete characterization of Birkhoff-James orthogonality in infinite dimensional normed space
Functional Analysis
2024-08-13 v3
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.
Keywords
Cite
@article{arxiv.1706.07713,
title = {A complete characterization of Birkhoff-James orthogonality in infinite dimensional normed space},
author = {Debmalya Sain and Kallol Paul and Arpita Mal},
journal= {arXiv preprint arXiv:1706.07713},
year = {2024}
}