$k$-bitransitive and compound operators on Banach spaces
Keywords: hypercyclic operators, diskcyclic operators, weakly mixing operators, direct sums
Published online: 2016-06-30
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 an operator to be $k$-bitransitive or compound. We give a relation between topologically mixing operators and compound operators. Also, we extend the Godefroy-Shapiro Criterion for topologically mixing operators to compound operators.