A Study on Properties of skew (n,m) Binormal Operators

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Published: 2024-01-18

Page: 12-21


Luketero Stephen Wanyonyi *

Department of Mathematics, Faculty of Science and Technology, University of Nairobi, Kenya.

Kikete Dennis Wabuya

Department of Mathematics, Faculty of Science and Technology, University of Nairobi, Kenya.

*Author to whom correspondence should be addressed.


Abstract

In this paper, the class of skew (n;m)-binormal operators acting on a Hilbert space (H) is introduced. An operator T \(\in\) B(H) is skew (n,m) binormal operators if it satisfies the condition (T*mTnTnT*m)T = T(TnT*mT*mTn). We investigate some of the basic properties of this class of operators. In particular, it has been shown that any scalar multiple of a skew (n,m) binormal operator is also skew (n,m) binormal. A counter example is provided to show that the class of (n;m) binormal operators is not in general contained in the class of skew (n;m) binormal operators. The concept of (n,m)-unitary quasiequivalence is introduced and shown to be an equivalence relation. It is further shown that if an operator T is skew (n,m)-binormal, and is unitarily equivalent to an operator S, then S is also skew (n,m)-binormal.

Keywords: Skew-(n,m)-binormal, isometric equivalence, (n,m)-unitary equivalence


How to Cite

Wanyonyi, L. S., & Wabuya, K. D. (2024). A Study on Properties of skew (n,m) Binormal Operators. Asian Journal of Pure and Applied Mathematics, 6(1), 12–21. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1930

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