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. © 2013 Elsevier Ltd.This work is supported in part by MEC and FEDER, Project MTM2010-14909. The first author was also supported by a grant from CONACYT.Jiménez-Munguía, RR.; Martínez-Avendaño, RA.; Peris Manguillot, A. (2013). Some questions about subspace-hypercyclic operators. Journal of Mathematical Analysis and Applications. 408:209-212. doi:10.1016/j.jmaa.2013.05.068S20921240