On Quasi-similarity of a product of Quasi-similar operators in Hilbert Spaces.

Abstract

In this paper we investigate the conditions under which two operators A and B are quasi-similar implies AB and BA are also quasi-similar. It is herein shown that if A and B satisfy the Putnam-Fuglede property and are quasi-similar with the intertwining quasiaffinities self adjoint, then AB and BA are also quasi-similar.

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

Keywords and phrases: Quasi-similarity, quasi-affinity and Putnam-Fuglede property.