On posinormality of weighted composition-differentiation operators on $H^2(\mathbb{D})$

Abstract

In this article, the posinormality and coposinormality of weighted composition-differentiation operators on Hardy space $H^2(\mathbb{D})$ are investigated. It is observed that while a composition-differentiation operator $D_{\phi,n}$ fails to be posinormal, the weighted composition-differentiation operator $D_{\psi,\phi,n}$ can be posinormal for specific choices of $\psi, \phi$. Some necessary conditions are obtained for posinormality and coposinormality of the operator $D_{\psi,\phi,n}$. Furthermore, the adjoint formula for this operator is derived which also helped us to examine some results regarding posinormality of this operator.