a1 Department of Mathematics, University of Puerto Rico, Mayagüez, Puerto Rico 00681 e-mail: email@example.com
Let E be a Banach space such that its dual E* is separable. We show that there exists a hypercyclic bounded operator T on E such that its adjoint T* is also hypercyclic on E*. We also exhibit a new kind of dual hypercyclic operator. Thus answers affirmatively two of the questions raised by Henrik Petersson in a recent paper.
(Received August 04 2006)
(Revised January 03 2007)
(Revised March 13 2007)
(Accepted March 19 2007)