Diskcyclicity of Sets of Operators and Applications

In this paper, we introduce and study the diskcyclicity and disk transitivity of a set of operators. We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity. As applications, we study the diskcyclicty of C0-semigroups and C-regularized groups.We show that a diskcyclic C0-semigroup exists on a complex topological vector space X if and only if dim（X） = 1 or dim（X） = ∞ and we prove that diskcyclicity and disk transitivity of C0-semigroups（resp C-regularized groups） are equivalent.