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A COMPLETE CHARACTERIZATION OF BIRKHOFF-JAMES ORTHOGONALITY IN INFINITE DIMENSIONAL NORMED SPACE

Sain, Debmalya and Paul, Kallol and Mal, Arpita (2018) A COMPLETE CHARACTERIZATION OF BIRKHOFF-JAMES ORTHOGONALITY IN INFINITE DIMENSIONAL NORMED SPACE. In: JOURNAL OF OPERATOR THEORY, 80 (2). pp. 399-413.

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Official URL: http://dx.doi.org/10.7900/jot.2017oct20.2190

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.

Item Type: Journal Article
Additional Information: Copy right for this article belong to THETA FOUNDATION
Keywords: Orthogonality; linear operators; norm attainment; smoothness
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 15 Nov 2018 14:11
Last Modified: 15 Nov 2018 14:11
URI: http://eprints.iisc.ac.in/id/eprint/61071

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