Supercyclic Properties of Extended Eigenoperators of the Differentiation Operator on the Space of Entire Functions

A continuous linear operator L defined on the space of entire functions \(\mathcal {H}({\mathbb {C}})\) $\mathcal{H}(\mathbb{C})$ is said to be an extended \(\lambda \) $\lambda$ -eigenoperator of the differentiation operator D provided \(DL=\lambda LD\) $DL=\lambda LD$ . Here we fully characterize when an extended \(\lambda \) $\lambda$ -eigenoperator of D is supercyclic, it has a hypercyclic subspace or it has a supercyclic subspace.