k–QUASI–A–PARANORMAL OPERATORS IN SEMI–HILBERTIAN SPACES

The purpose of this study is to extend the notion of (n;m)-power
normal bounded operator of Hilbert space to a nite 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.