{"title":"Hypercyclicity, Supercyclicity and Cyclicity of Composition Operators on L p Spaces","authors":"V. K. Srivastava, H. Chandra","doi":"10.18311/JIMS/2019/22578","DOIUrl":null,"url":null,"abstract":"In this paper, we discuss hypercyclicity, supercyclicity and cyclicity of composition operators on l p (1 ≤ p < ∞). We prove that no composition operator is hypercyclic on l p . Further, we also prove that C Φ : l p → l p is supercyclic if and only if Φ is injective and Φ n has no fixed point in N, for any n ∈ N. We also give a sufficient condition and some necessary conditions for cyclicity of composition operator.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":"86 1","pages":"187-198"},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18311/JIMS/2019/22578","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
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Abstract
In this paper, we discuss hypercyclicity, supercyclicity and cyclicity of composition operators on l p (1 ≤ p < ∞). We prove that no composition operator is hypercyclic on l p . Further, we also prove that C Φ : l p → l p is supercyclic if and only if Φ is injective and Φ n has no fixed point in N, for any n ∈ N. We also give a sufficient condition and some necessary conditions for cyclicity of composition operator.
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The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.
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