ON THE EXISTENCE OF SUBSPACE-DISKCYCLIC C0-SEMIGROUPS AND SOME CRITERIA

In this paper,  we prove the existance of subspace-diskcyclic $C_{0}$-semigroups   on any infinite-dimensional   separable Banach space.  We state that diskcyclic $C_{0}$-semigroups are subspace-diskcyclic. Also, we establish some criteria for subspace-diskcyclic $C_{0}$-semigroups. Most of these criteria  are based on non-empty relatively open sets  and some of them are based on dense sets.