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arXiv · 2006.06440

Some remarks on orthogonality of bounded linear operators

Anubhab Ray·Debmalya Sain·Subhrajit Dey·Kallol Paul
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Abstract

We explore the relation between the orthogonality of bounded linear operators in the space of operators and that of elements in the ground space. To be precise, we study if $ T, A \in \mathbb{L}(\mathbb{X}, \mathbb{Y}) $ satisfy $ T \bot_B A,$ then whether there exists $ x \in \mathbb{X} $ such that $ Tx\bot_B Ax$ with $ \|x\| =1, \|Tx\| = \|T\|$, where $\mathbb{X}, \mathbb{Y} $ are normed linear spaces. In this context, we introduce the notion of Property $ P_n $ for a Banach space and illustrate its connection with orthogonality of a bounded linear operator between Banach spaces. We further study Property $ P_n $ for various polyhedral Banach spaces.

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Anubhab Ray, Debmalya Sain, Subhrajit Dey, Kallol Paul. 2020-06-11. Some remarks on orthogonality of bounded linear operators. https://arxiv.org/abs/2006.06440

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