Some questions about 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 . We show examples that answer some questions posed by H. Rezaei (2013) [7]. In particular, we provide an example of an operator T such that Orb ( T , x ) ∩ M is somewhere dense in M , but it is not everywhere dense in M .