Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms

IF 0.7 2区数学 Q2 MATHEMATICS Collectanea Mathematica Pub Date : 2024-03-12 DOI:10.1007/s13348-024-00437-9

引用次数: 0

Abstract

An investigation is made of the generalized Cesàro operators $C_t$ , for $t\in [0,1]$ , when they act on the space $H({{\mathbb {D}}})$ of holomorphic functions on the open unit disc ${{\mathbb {D}}}$ , on the Banach space $H^\infty $ of bounded analytic functions and on the weighted Banach spaces $H_v^\infty $ and $H_v^0$ with their sup-norms. Of particular interest are the continuity, compactness, spectrum and point spectrum of $C_t$ as well as their linear dynamics and mean ergodicity.

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加权巴拿赫解析函数超规范空间中的广义塞萨罗算子

Abstract 本文对广义 Cesàro 算子（C_t\ ）进行了研究，对于 $t\in [0,1]$, 当它们作用于开放单位圆盘 ${\mathbb {D}}) 上的全纯函数空间 \(H({\mathbb {D}}) 时、有界解析函数的巴拿赫空间（H^\infty \）上，以及加权巴拿赫空间（H_v^\infty \）和（H_v^0\）及其超规范上。特别令人感兴趣的是\(C_t$的连续性、紧凑性、谱和点谱，以及它们的线性动力学和平均遍历性。

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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来源期刊

Collectanea Mathematica 数学-数学

CiteScore

2.70

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Collectanea Mathematica publishes original research peer reviewed papers of high quality in all fields of pure and applied mathematics. It is an international journal of the University of Barcelona and the oldest mathematical journal in Spain. It was founded in 1948 by José M. Orts. Previously self-published by the Institut de Matemàtica (IMUB) of the Universitat de Barcelona, as of 2011 it is published by Springer.

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