COMMUTING TUPLES OF (n, m)-POWER NORMAL OPERATORS IN HILBERT SPACES

The purpose of this study is to extend the notion of (n, m)-power normal bounded operator of Hilbert space to a finite set of commuting such operators. Similar studies for other classes of operators exist in the literature. The purpose of this paper is to introduce and study the structure of certain special types of several variable operators on a Hilbert space named joint (n, m)-power normal multioperators. This is a generalization of the classes of joint normal and joint n-normal multioperators. We consider a multivariable generalization of these single variable n-normal and (n, m)-normal operators and explore some of their basic properties.