On Unitary Quasi-equivalence and Partial Isometry Operators in Hilbert Spaces
Anyembe Lilian
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
Unitary quasi-equivalence has been shown to be an equivalence relation. Similarly, unitary quasi-equivalence has been proven to preserve normality, hyponormality and binormality of operators. However, the properties of unitary quasi-equivalence and partial isometric operators have not been established. In this paper therefore, the study aims to determine the properties of unitary quasi-equivalence and isometry, co-isometry and partial isometry operators.
Keywords: Unitary quasi-equivalence, isometry, co-isometry, partial isometry, operator and Hilbert space