Asian Journal of Pure and Applied Mathematics

A Study on Properties of (n;m)- Hyponormal Operators

Kikete, D. Wabuya *

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

Luketero, S. Wanyonyi

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

Mile, J. Kitheka

Kiriri Womens University of Science and Technology, Kenya.

Wafula, A. W. Wanyonyi

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

*Author to whom correspondence should be addressed.

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Abstract

This paper looks at the properties of (n;m)- hyponormal operators. We show that for an operator A that is (n;m)- hyponormal, and it is equivalent under an isometry to an operator B, then B is also (n;m)- hyponormal. Additionally, the concept of (n;m)-unitary quasiequivalence is introduced, and it is also shown that if an operator A is (n;m)- hyponormal, and is (n;m)-unitary quasiequivalence to an operator B, then B is also (n;m)- hyponormal.

Keywords: (n;m)-hyponormal, isometric equivalence, (n;m)-unitary quasiequivalence

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