On the existence of subspace-diskcyclic $C_{0}$-semigroups and some criteria

Abstract

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.

Keywords

• subspace-diskcyclicity
• diskcyclicity
• $c_{0}$-semigroups