ON QUASI-INVERTIBILITY AND QUASI-SIMILARITY OF OPERATORS IN HILBERT SPACES.

Abstract

It is a well known fact in operator Theory that if A and B are operators with at least one of them invertible then AB and BA are similar operators.  In this paper we prove an analogous result about quasi-invertible operators A and B. We thus show that if A and B are quasi-invertible then AB and BA are quasi-similar. We also deduce a number of corollaries about spectra and essential spectra of AB and BA.

AMS subject classification: 47B47, 47A30, 47B20

Key words and phrases: quasi-invertibility and quasi-similarity.