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Hypercyclic Operators on Vector-Valued Hardy Spaces

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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 \(H^2.\)

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Yasouj University, Yasouj, 75914-74831, Iran

    Hamid Rezaei & Javad Amini Ab Alvan

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  1. Hamid Rezaei
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  2. Javad Amini Ab Alvan
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Correspondence to Hamid Rezaei.

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Rezaei, H., Amini Ab Alvan, J. Hypercyclic Operators on Vector-Valued Hardy Spaces. Iran J Sci Technol Trans Sci 43, 875–881 (2019). https://doi.org/10.1007/s40995-018-0547-3

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  • DOI: https://doi.org/10.1007/s40995-018-0547-3

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