Debmalya Sain, Kallol Paul, Arpita Mal
Published 2017-06-23Version 1
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.
On some geometric properties of operator spaces
Birkhoff-James orthogonality to a subspace of operators defined between Banach spaces
Preduals and complementation of spaces of bounded linear operators
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