Ergodic properties of multiplication and weighted composition operators on spaces of holomorphic functions

Pub Date : 2024-03-12 DOI:10.1002/mana.202300430

Daniel Santacreu

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Abstract

We obtain different results about the mean ergodicity of weighted composition operators when acting on the spaces $H (B)$ , $H_{b} (B)$ , and $H^{\infty} (B)$ , where $B$ is the open unit ball of a Banach space, as well as about the compactness and the mean ergodicity of the multiplication operator. This study relates these properties of the operators with properties of the symbol and the weight defining such operators.

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全形函数空间上乘法和加权合成算子的遍历性质

我们得到了关于加权合成算子作用于空间 H(B)$H(B)$、Hb(B)$H_b(B)$ 和 H∞(B)$H^\infty (B)$ （其中 B$B$ 是巴拿赫空间的开单位球）时的平均遍历性的不同结果，以及关于乘法算子的紧凑性和平均遍历性的不同结果。本研究将这些算子的性质与定义这些算子的符号和权重的性质联系起来。

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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