A NOTE ON SIMILARITY, ALMOST-SIMILARITY AND EQUIVALENCE OF OPERATORS

B. M. Nzimbi (Kenya), G. P. Pokhariyal (Kenya) and J. M. Khalagai (Kenya)

Received May 29, 2007; Revised October 12, 2007

Abstract

The almost-similar and similar relations between operators on finite-dimensional Hilbert spaces are investigated. It is shown that almost-similar operators share some properties with some other classes of operators. Various results on almost-similarity and similarity are proved. An attempt is made to classify those operators where almost-similarity implies similarity. We investigate some properties of corresponding parts of operators which enjoy these equivalence relations.

Keywords and phrases: almost-similar, similar, hermitian, isometric.