Hypercyclic Operators on Vector-Valued Hardy Spaces

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 $$H^2.$$