Norm-Attainability and Range-Kernel Orthogonality of Elementary Operators

Year 2018, Volume: 1 Issue: 2, 91 - 98, 24.12.2018

Bernard Okelo

https://doi.org/10.33434/cams.442556

Abstract

Various aspects of elementary operators have been characterized by many mathematicians. In this paper, we consider norm-attainability and orthogonality of these operators in Banach spaces. Characterizations and generalizations of norm-attainability and orthogonality are given in details. 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 Banach spaces.

Keywords

Range-Kernel orthogonality, Elementary operator

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