A Note on Quasi-Similarity of Operators in Hilbert Spaces

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Date

2016

Journal Title

Journal ISSN

Volume Title

Publisher

Chuka University

Abstract

This paper reports on the notion of Quasi-similarity of bounded linear operators in Hilbert Spaces, defines a quasi-affinity from one Hilbert Space H to K and discusses results on quasi-affinities. It has been shown that on a finite dimensional Hilbert Space, quasi-similarity is an equivalence relation; it is reflexive, symmetric and transitive. Using the definition of commutants of two operators, an alternative result is given to show that quasi-similarity is an equivalence relation on an infinite dimensional Hilbert Space. The relationship between quasi-similarity and almost similarity equivalence relations in Hilbert Spaces using hermitian and normal operators is established.

Description

swmusundi@chuka.ac.ke

Keywords

Quasi-similarity, Quasi affinities, Equivalence Relations, Commutants

Citation

Sitati, I.N., & Musundi, S.W. (2016). A note on quasi-similarity of operators in Hilbert spaces. In: Isutsa, D.K. and Githae, E.W. Proceedings of the Second Chuka University International Research Conference held in Chuka University, Chuka, Kenya from 28th to 30th October, 2015. 357-363 pp.