  In this this paper, we introduce new classes of operators in complex Banach
spaces, which we call k-bitransitive operators and compound operators to study
the direct sum of diskcyclic operators. We create a set of sufficient
conditions for k-bitransitivity and compound. We show the relation between
topologically mixing operators and compound operators. Also, we extend the
Godefroy-Shapiro Criterion for topologically mixing operators to compound
operators.
