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

Abstract

The purpose of this paper is to introduce and study the structure of p-tuple of $(n,m)$ - $\mathcal{D}$ -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- $\mathcal{D}$ -normal and $(n,m)$ - $\mathcal{D}$ -normal operators and explore some of their basic properties.