某些解析函数空间上的加权后移动力学

IF 1.1 3区 数学 Q1 MATHEMATICS
Bibhash Kumar Das, Aneesh Mundayadan
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引用次数: 0

摘要

我们引入了单位圆盘上解析函数的巴拿赫空间 \(\ell ^p_{a,b}\) 和 \(c_{0,a,b}\),它们的归一化 Schauder 基由形式为 \(f_n(z)=(a_n+b_nz)z^n 的多项式组成、~~n\ge 0\), 其中假设 \(\{f_n\}\) 分别等价于 \(\ell ^p\) 和 \(c_0\) 的标准基。我们研究了这些空间上的加权后移算子 \(B_w\),得到了 \(B_w\)有界的必要条件和充分条件,并证明了在\(\{a_n\}\)和\(\{b_n\}\)的一些温和假设下,算子 \(B_w\)类似于序列空间 \(\ell^p\)或 \(c_0\)上加权后移的紧凑扰动。此外,我们还研究了 \(B_w\) 的超循环性、混合性和混沌性,并通过计算其基本谱建立了 \(B_w\) 的超循环子空间的存在性。对于 \(\ell ^p_{a,b}\) 和 \(c_{0,a,b}\) 上的\(B_w\) 函数,我们也得到了类似的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dynamics of Weighted Backward Shifts on Certain Analytic Function Spaces

We introduce the Banach spaces \(\ell ^p_{a,b}\) and \(c_{0,a,b}\), of analytic functions on the unit disc, having normalized Schauder bases consisting of polynomials of the form \(f_n(z)=(a_n+b_nz)z^n, ~~n\ge 0\), where \(\{f_n\}\) is assumed to be equivalent to the standard basis in \(\ell ^p\) and \(c_0\), respectively. We study the weighted backward shift operator \(B_w\) on these spaces, and obtain necessary and sufficient conditions for \(B_w\) to be bounded, and prove that, under some mild assumptions on \(\{a_n\}\) and \(\{b_n\}\), the operator \(B_w\) is similar to a compact perturbation of a weighted backward shift on the sequence spaces \(\ell ^p\) or \(c_0\). Further, we study the hypercyclicity, mixing, and chaos of \(B_w\), and establish the existence of hypercyclic subspaces for \(B_w\) by computing its essential spectrum. Similar results are obtained for a function of \(B_w\) on \(\ell ^p_{a,b}\) and \(c_{0,a,b}\).

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来源期刊
Results in Mathematics
Results in Mathematics 数学-数学
CiteScore
1.90
自引率
4.50%
发文量
198
审稿时长
6-12 weeks
期刊介绍: Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.
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