Abstract
We introduce and discuss a class of operators, to be referred to as oper- ators close to isometries. The Bergman-type operators, 2-hyperexpansions, expansive p- isometries, and certain alternating hyperexpansions are main examples of such operators. We establish a few decomposition theorems for operators close to isometries. Applications are given to the theory of p-isometries and of hyperexpansive operators. 1. Preliminaries. In this paper, we discuss the following fundamental problems from single-variable operator theory. If S inB(H) is a completely non-unitary left-invertible operator, under what conditions does
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