Cesàro operators on the space of analytic functions with logarithmic growth

arXiv - MATH - Functional Analysis Pub Date : 2024-09-17 DOI:arxiv-2409.11371

José Bonet

引用次数: 0

Abstract

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.

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具有对数增长的解析函数空间上的塞萨罗算子

当 Ces\`arooperators 作用于复数平面的开放单位圆盘 $\mathbb{D}$ 上对数增长的解析函数空间 $VH(\mathbb{D})$ 时，研究了 Ces\`arooperators 的连续性、紧凑性、频谱和遍历性质。VH(\mathbb{D})$空间是具有紧凑链接映射的解析函数的加权巴拿赫空间的可数归纳极限。它是由 Taskinen 和 Jasiczak 引入并研究的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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arXiv - MATH - Functional Analysis

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