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On orthogonality of elementary operators in norm-attainable classes. (English) Zbl 1509.47051

Summary: Various notions of orthogonality of elementary operators have been characterized by many mathematicians in different classes. In this paper, we characterize orthogonality of these operators in norm-attainable classes. We first give necessary and sufficient conditions for norm-attainability of Hilbert space operators then we give results on orthogonality of the range and the kernel of elementary operators when they are implemented by norm-attainable operators in norm-attainable classes.

MSC:

47B47 Commutators, derivations, elementary operators, etc.
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
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References:

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