On the Quasisimilarity of Subnormal Operators

This paper deals with the following problem: whether the quasisimilarity of subnormal operators would imply the equality of their essential spectrum. It is shown that if a subnormal operator is quasisimilar to a quasinormal operator, then they have the same essential spectrum. Furthermore, if the quasinormal operator in this case is almost normal, then they are unitarily equivalent up to a compact perturbation.