{"title":"Weak Supercyclicity—An Expository Survey","authors":"Carlos S. Kubrusly","doi":"10.1007/s00025-024-02205-4","DOIUrl":null,"url":null,"abstract":"<p>This is an exposition on supercyclicity and weak supercyclicity, especially designed to advance further developments in weakly supercyclicity, which is a recent research field showing significant momentum during the past two decades. For operators on a normed space, the present paper explores the relationship among supercyclicity and three versions of weak supercyclicity, namely, weak l-sequential, weak sequential, and weak supercyclicities, and their connection with strong stability, weak stability, and weak quasistability. A survey of the literature on weak supercyclicity is followed by an analysis of the interplay between supercyclicity and strong stability, as well as between weak supercyclicity and weak stability. A description of the spectrum of weakly l-sequentially supercyclic operators is also given.\n</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00025-024-02205-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This is an exposition on supercyclicity and weak supercyclicity, especially designed to advance further developments in weakly supercyclicity, which is a recent research field showing significant momentum during the past two decades. For operators on a normed space, the present paper explores the relationship among supercyclicity and three versions of weak supercyclicity, namely, weak l-sequential, weak sequential, and weak supercyclicities, and their connection with strong stability, weak stability, and weak quasistability. A survey of the literature on weak supercyclicity is followed by an analysis of the interplay between supercyclicity and strong stability, as well as between weak supercyclicity and weak stability. A description of the spectrum of weakly l-sequentially supercyclic operators is also given.
这是一篇关于超周期性和弱超周期性的论述,特别旨在推动弱超周期性的进一步发展,而弱超周期性是近二十年来势头强劲的最新研究领域。对于规范空间上的算子,本文探讨了超周期性与弱超周期性的三个版本,即弱 l 序列性、弱序列性和弱超周期性之间的关系,以及它们与强稳定性、弱稳定性和弱准稳定性之间的联系。在对有关弱超周期性的文献进行考察之后,分析了超周期性与强稳定性之间以及弱超周期性与弱稳定性之间的相互作用。此外,还给出了弱 l 序列超周期算子谱的描述。
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.