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.

中文翻译：

---

具有超范数的解析函数加权Banach空间中的广义Cesàro算子

摘要

研究了广义塞萨罗算子\(C_t\)，对于\(t\in [0,1]\)，当它们作用于空间\(H({{\mathbb {D}}})\时)开单位圆盘\({{\mathbb {D}}}\)上的全纯函数、有界解析函数的 Banach 空间\(H^\infty \)以及加权 Banach 空间\(H_v^\ infty \)和\(H_v^0\)及其超范数。特别令人感兴趣的是\(C_t\)的连续性、紧致性、谱和点谱以及它们的线性动力学和平均遍历性。