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

TL;DR

This paper characterizes when convolution and Toeplitz operators on power series spaces are topologizable and power bounded, providing necessary conditions and extending results to classical function spaces.

Contribution

It offers new characterizations and necessary conditions for topologizability and power boundedness of convolution and Toeplitz operators on various power series spaces.

Findings

Necessary conditions for Toeplitz operator m-topologizability

Characterization of power boundedness on specific power series spaces

Extension of results to classical spaces like H(C) and H(D)

Abstract

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 $\Lambda_{1}(n)$ and $\Lambda_{\infty}(n)$, and consequently on $H(\mathbb{C})$ and $H(\mathbb{D})$.