Powers of Convex-Cyclic Operators

الملخص EN

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).