A note on m-Isometric and Quasi-m-isometric operators

In this paper we characterize [Formula: see text]-isometric and quasi-[Formula: see text]-isometric weighted conditional type (WCT) operators on the Hilbert space [Formula: see text]. Also, we prove that the subclasses of [Formula: see text]-isometric and quasi-[Formula: see text]-isometric of normal WCT operators are coincided. Moreover, we get that quasi-m-isometry WCT operators have finite spectrum. Consequently, we have the results for multiplication operators. Indeed, we find that for [Formula: see text], a multiplication operator [Formula: see text] is [Formula: see text]-isometric (quasi-[Formula: see text]-isometric) if and only if it is isometric (quasi-isometric). Some examples are provided to illustrate our results.