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 C 0 -semigroups and C -regularized groups. We show that a diskcyclic C 0 -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 C 0 -semigroups (resp C -regularized groups) are equivalent.