some notes on subspace convex-cyclicity

A bounded linear operator t on banach space x is subspace convex-cyclic for a subspace m if there exists a vector x ∈ x such that co(orb(t, x)) ∩ m is dense in m. we construct examples of subspace convex-cyclic operator that is not convex-cyclic. in particular, we prove that every convex-cyclic operator on the separable banach space x is a subspace convex-cyclic operator for some pure subspace m of x.