On The extension Bi-Normality of Linear Operators

Anas A. Hijab; Elaf S. Abdulwahid

doi:10.24996/ijs.2023.64.4.24

Authors

Anas A. Hijab Mathematics Department, College of Education for Pure Sciences, Tikrit University, Salah Al Deen, Iraq https://orcid.org/0000-0001-5001-1937
Elaf Sabah Abdulwahid Mathematics Department, College of Education for Women, Tikrit University, Salah Al Deen, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.4.24

Keywords:

Bi-normality set, Unitary operator, Quasi-similar operator, Similar operator, Aluthge transformation

Abstract

In this paper, we introduce the bi-normality set, denoted by , which is an extension of the normality set, denoted by for any operators in the Banach algebra . Furthermore, we show some interesting properties and remarkable results. Finally, we prove that it is not invariant via some transpose linear operators.