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.


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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Campbell SL. Linear operators for which T*T and TT* commute. Proceedings of the American Mathematical Society. 1972;34(1):177-80.

Campbell S. Linear operators for which T*T and TT* commute (II). Paci c J. Math. 1974;53:355{361.

Brown A. The unitary equivalence of binormal operators. American Journal of Mathematics. 1954;76(2):414- 434.

Garcia S, Wogen W. Some new classes of complex symmetric operators. Transactions of the American Mathematical Society. 2010;362(11):6065-6077.

Jung S, Kim Y, Ko E. Characterizations of binormal composition operators with linear fractional symbols on H2. Applied Mathematics and Computation. 2015 Jun 15;261:252-63.

Jibril AAS. On n-power normal operators. The Arabian Journal of Science and Engineering. 2008;33(2A):247-251.

Abood EH, Al-loz MA. On some generalizations of (n,m)-normal powers operators on Hilbert space. Journal of Progressive Research in Mathematics(JPRM). 2016;7(3):1063-1070.

Wabuya K, Wanyonyi SL, Mile JK, Wanyonyi AWW. Classes of operators related to binormal operators. Scienti c African. 2023;22:e01973.

Meenambiku K, Seshaiah CV, Sivamani N. On Square Binormal and square n-binormal Operators. International Journal of Innovative Technology and Exploring Engineering (IJITEE). 2019;8(7):1669{1672.

Abdul Hussein SS, Ali Shubber H. Spectral theory of (n,m)-normal operators on hilbert space. Journal of Interdisciplinary Mathematics. 2021;24(7).

Abood EH, MA Al-loz. On some generalization of normal operators on Hilbert space. Iraqi Journal of Science. 2015;56(2C):1786-1794.