Linear operators with infinite entropy

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Brian, Will¹  Kelly, James P.² 

[1] Univ North Carolina Charlotte, Dept Math & Stat, 9201 Univ City Blvd, Charlotte, NC 28223 USA

[2] Christopher Newport Univ, Dept Math, Newport News, VA 23606 USA

关键词: Translation operators;    Weighted Lebesgue space;    Topological entropy;   

DOI  :  10.1016/j.jmaa.2020.123981

来源: Elsevier

【 摘 要 】

We examine the chaotic behavior of certain continuous linear operators on infinite-dimensional Banach spaces, and provide several equivalent characterizations of when these operators have infinite topological entropy. For example, it is shown that infinite topological entropy is equivalent to non-zero topological entropy for translation operators on weighted Lebesgue function spaces. In particular, finite non-zero entropy is impossible for this class of operators, which answers a question raised by Yin and Wei. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free