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Abstract. In the present paper we investigate conditions under which a holomorphic self-map of the open unit disk induces a hypercyclic weighted composition operator in the space of holomorphic functions.

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a b s t r a c tA bounded linear operator T on a Banach space X is called subspace-hypercyclic for aIn this case we show that p(T ) has a relatively dense range for every real or complex polynomial p, which in turn answers a question posed in Madore and Martinez-Avendano (2011) [8]. As a consequence, the algebraic structure of the set of subspace-hypercyclic vectors can be described.