Powers of Convex-Cyclic Operators

A bounded operator T on a Banach space X is convex cyclic if there exists a vector x such that the convex hull generated by the orbit {T(n)x}(n >= 0) is dense in X. In this note we study some questions concerned with convex-cyclic operators. We provide an example of a convex-cyclic operator T such that the power T-n fails to be convex cyclic. Using this result we solve three questions posed by Rezaei (2013).