On a class of m-Isometric and Quasi-m-isometric operators

Abstract

In this paper we characterize $m$-isometric and quasi-$m$-isometric weighted conditional type (WCT) operators on the Hilbert space $L^2(\mu)$. Also, we prove that the subclasses of $m$-isometric and quasi-$m$-isometric of normal WCT operators are coincide. Specially we have the results for multiplication operators. Indeed, we find that for $m\geq 2$, a multiplication operator $M_u$ is $m$-isometric (quasi-$m$-isometric) if and only if it is isometric (quasi-isometric). Some examples are provided to illustrate our results.