Hypercyclicity, Supercyclicity and Cyclicity of Composition Operators on L p Spaces

Q4 Mathematics

Journal of the Indian Mathematical Society Pub Date : 2019-01-01 DOI:10.18311/JIMS/2019/22578

V. K. Srivastava, H. Chandra

引用次数: 0

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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lp空间上复合算子的超环性、超环性和环性

讨论了l p(1≤p <∞)上复合算子的超环性、超环性和环性。证明了l p上没有复合算子是超循环的。进一步证明了对于任意n∈n，当且仅当Φ是内射且Φ n在n中没有不动点时，C Φ: l p→l p是超循环的，并给出了复合算子循环的充分条件和必要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the Indian Mathematical Society Mathematics-Mathematics (all)

CiteScore

0.50

自引率

0.00%

发文量

期刊介绍： 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.