Notes on subspace-hypercyclic operators

A bounded linear operator T on a Banach space X is called subspace-hypercyclic for a subspace M if orb(T,x)∩M is dense in M for a vector x∈M. In 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.