Cesàro operators on the space of analytic functions with logarithmic growth

Continuity, compactness, the spectrum and ergodic properties of Ces\`aro operators are investigated when they act on the space $VH(\mathbb{D})$ of analytic functions with logarithmic growth on the open unit disc $\mathbb{D}$ of the complex plane. The space $VH(\mathbb{D})$ is a countable inductive limit of weighted Banach spaces of analytic functions with compact linking maps. It was introduced and studied by Taskinen and also by Jasiczak.