A note on -Isometries and self-similarity of operators on Hilbert spaces

Abstract

In this paper we investigate -isometries and related classes of operators. We will also introduce and study the notions of similitudes, self-similarity and -metric equivalence relations of operators. It will be shown that self-similarity implies -metric equivalence of operators. We will characterize -isometric and -unitary and prove that quasisimilar -isometries are unitarily equivalent.