ON SUBSPACE BALANCED CONVEX-CYCLIC OPERATORS

Let X be a separable Banach space and M be a subspace of X. A bounded Linear operator T on X is subspace balanced convex-cyclic for a subspace M, if there exists a vector x∈X such that the intersection of balanced convex hull of orb(T,x) with M is dense in M. We give an example of subspace balanced convex-cyclic operator that is not balanced convex-cyclic. Also we give an improvement of the Kitailike criterion for subspace balanced convex-cyclicity and bring on with the Hahn-Banach characterization for subspace balanced convex-cyclicity.