- Communications in Advanced Mathematical Sciences
- Vol: 1 Issue: 2
- Norm-Attainability and Range-Kernel Orthogonality of Elementary Operators
Norm-Attainability and Range-Kernel Orthogonality of Elementary Operators
Authors : Bernard Okelo
Pages : 91-98
Doi:10.33434/cams.442556
View : 7 | Download : 4
Publication Date : 2018-12-24
Article Type : Research
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