On n-quasi-m-isometric operators

Abstract

We introduce the class of [Formula: see text]-quasi-[Formula: see text]-isometric operators on Hilbert space. This generalizes the class of [Formula: see text]-isometric operators on Hilbert space introduced by Agler and Stankus. An operator [Formula: see text] is said to be [Formula: see text]-quasi-[Formula: see text]-isometric if [Formula: see text] In this paper [Formula: see text] matrix representation of a [Formula: see text]-quasi-[Formula: see text]-isometric operator is given. Using this representation we establish some basic properties of this class of operators.