Cesàro operators on the space of analytic functions with logarithmic growth
Annales Polonici Mathematici
MSC: Primary 47B91; Secondary 46E10, 46E15, 47A10, 47A16, 47A35, 47B38
DOI: 10.4064/ap240429-16-9
Published online: 26 June 2025
Abstract
Continuity, compactness, the spectrum and ergodic properties of Cesàro 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.
