Topologizability and Power Boundedness of Convolutions and Toeplitz Operators on Power Series Spaces

We characterize the topologizability and power boundedness of convolution and dual convolution operators on power series spaces. We determine necessary conditions for a Toeplitz operator to be m-topologizable, and power bounded on ${\mathrm{\Lambda }}_1(n)$ and ${\mathrm{\Lambda }}_{\mathrm{\infty }}(n)$, and consequently on $H(\mathbb{C})$ and $H(\mathbb{D})$.