On Browder Spectrum and Quasisimilarity of M-hyponormal Operators in Hilbert Spaces
Kamau Faith
Department of Physical Sciences, Chuka university, P.O Box 109-60400, Chuka, Kenya.
Musundi Sammy Wabomba *
Department of Physical Sciences, Chuka university, P.O Box 109-60400, Chuka, Kenya.
Kinyanjui Jeremiah Ndung’u
Department of Pure & Applied Sciences, Kirinyaga University, P.O Box 143-10300, Kerugoya, Kenya.
*Author to whom correspondence should be addressed.
Abstract
The spectrum of operators and quasisimilarity of m-hyponormal operators in Hilbert Spaces has been extensively studied. It has been shown that quasisimilarity of m-hyponormal operators have equal spectrum, equal Essential Spectrum and equal Weyl Spectrum. However, the consideration of equality of the Browder spectrum for m-hyponormal operators together with quasisimilarity has not been fully determined. Therefore, this study aims to consider the quasisimilarity of m-hyponormal operators and determine the conditions under which quasisimilarity of m-hyponormal operators yields equal Browder spectrum.
Keywords: Quasisimilarity, browder spectrum, biquasitriangular, m-hyponormal operator