Higher order $(n,m)$-Drazin normal operators

Abstract

The purpose of this paper is to introduce and study the structure of p-tuple of $(n,m)$ ( n , m ) -$\mathcal{D}$ D -normal operators. This is a generalization of the class of p-tuple of n-normal operators. We consider a generalization of these single variable n-$\mathcal{D}$ D -normal and $(n,m)$ ( n , m ) -$\mathcal{D}$ D -normal operators and explore some of their basic properties.