Nzimbi, B. M. 1Luketero, S. W.1Sitati, I. N. 2Musundi, S.W. 3Mwenda, E 32020-10-012020-10-012016-06Pioneer Journal of Mathematics and Mathematical Scienceshttp://www.pspchv.com/content_PJMMS.htmlhttp://repository.chuka.ac.ke/handle/chuka/903In this paper, we investigate almost-similarity relation, metric equivalence and other relations of operators on Hilbert spaces. We characterize almost-similar, metrically equivalent operators. Roughly speaking, we consider two operators to be “equivalent” if they are “close” to each other in some sense. We establish some spectral invariants with respect to each of these equivalence relations.enQuasiaffinityalmost similarmetrically equivalentalmost unitary equivalencequasiunitaryHilbert-Schmidttrace-classArticle