Notes on subspace-hypercyclic operators

A bounded linear operator T on a Banach space X is called subspace-hypercyclic for a subspace M if o r b ( 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.