Hypercyclic Operators on Vector-Valued Hardy Spaces

Research Paper
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Abstract

Let T be a bounded linear operator on a Banach space X and \(\varphi\) be an analytic self-map of the unit disk \({\mathbb {D}}.\) We study the hypercyclic property of bilateral composition operator \(C_{\varphi , T}\colon f \rightarrow T \circ f \circ \varphi\) on the vector-valued Hardy space \(H^2(X).\) In particular, we show \(C_{\varphi }\) is hypercyclic on \(H^2(X)\) if and only if \(C_{\varphi }\) is hypercyclic on the scalar-valued Hardy space \(H^2.\)

Keywords

Hypercyclic operator Vector-valued Hardy space 

Mathematics Subject Classification

Primary 47A16 Secondary 47B48 

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Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesYasouj UniversityYasoujIran

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