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arXiv · 1810.04845

Some remarks on Birkhoff-James orthogonality of linear operators

Debmalya Sain·Kallol Paul·Arpita Mal
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Abstract

We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and improve some of the recent results in this context. In particular, we obtain a characterization of Euclidean spaces and also prove that it is possible to retrieve the norm of a compact (bounded) linear operator (functional) in terms of its Birkhoff-James orthogonality set. We also present some best approximation type results in the space of bounded linear operators.

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Debmalya Sain, Kallol Paul, Arpita Mal. 2018-10-11. Some remarks on Birkhoff-James orthogonality of linear operators. https://arxiv.org/abs/1810.04845

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