Journal of Operator Theory

Volume 80, Issue 2, Fall 2018 pp. 399-413.

A complete characterization of Birkhoff-James orthogonality in infinite dimensional normed space

Authors: Debmalya Sain (1), Kallol Paul (2), and Arpita Mal (3)
Author institution: (1) Department of Mathematics, Indian Institute of Science, Bengaluru, 560012, India
(2) Department of Mathematics, Jadavpur University, Kolkata, 700032, India
(3) Department of Mathematics, Jadavpur University, Kolkata, 700032, India

Summary: 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.

DOI: http://dx.doi.org/10.7900/jot.2017oct20.2190
Keywords: orthogonality, linear operators, norm attainment, smoothness

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