## Taiwanese Journal of Mathematics

- Taiwanese J. Math.
- Advance publication (2019), 12 pages.

### On Orthogonality of Elementary Operators in Norm-attainable Classes

#### Abstract

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.

#### Article information

**Source**

Taiwanese J. Math., Advance publication (2019), 12 pages.

**Dates**

First available in Project Euclid: 7 May 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.twjm/1557194426

**Digital Object Identifier**

doi:10.11650/tjm/190502

**Subjects**

Primary: 47B47: Commutators, derivations, elementary operators, etc.

Secondary: 47A30: Norms (inequalities, more than one norm, etc.)

**Keywords**

norm-attainable class range-kernel orthogonality elementary operator

#### Citation

Okelo, Nyaare Benard. On Orthogonality of Elementary Operators in Norm-attainable Classes. Taiwanese J. Math., advance publication, 7 May 2019. doi:10.11650/tjm/190502. https://projecteuclid.org/euclid.twjm/1557194426