On Unitary Quasi-Equivalence and w-Hyponormal Operators In Hilbert Spaces
Kennedy Kibe Karanu *
Department of Pure and Applied Sciences, Kirinyaga University, P. O. Box 143-10300, Kerugoya, Kenya.
Zachary Kayiita Kaunda
Department of Pure and Applied Sciences, Kirinyaga University, P. O. Box 143-10300, Kerugoya, Kenya.
Kinyanjui Jeremiah Ndung’u
Department of Pure and Applied Sciences, Kirinyaga University, P. O. Box 143-10300, Kerugoya, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the properties of unitary quasi-equivalence on the class of w-hyponormal operators are presented using the Aluthge transform and polar decomposition property. We show that for any two unitary quasi-equivalent operators, F and G, if one is w-hyponormal, then the other operator is also w-hyponormal. This result also holds for p-hyponormal and log-hyponormal operators.
Keywords: Hilbert space, unitary quasi-equivalence, w-hyponormal, p-hyponormal, log-hyponormal