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) boolean AND M is dense in M for a vector x is an element of 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. (C) 2012 Elsevier Inc. All rights reserved.