‎Some notes on subspace convex-cyclicity

Abstract

‎A bounded linear operator $T$ on Banach space $X$ is subspace convex-cyclic for a subspace $M$‎

‎if there exists a vector $x \in M$ such that $Co(orb(T‎, ‎x)) \cap M$ 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 $X$‎.‎