Hypercyclicity of the tensor products of multiplication operators on Hardy spaces

In this paper, we give a necessary and sufficient condition for the tensor product of two adjoints of multiplication hypercyclic operators to be mixing and chaotic. These results partially answer a question posed by Félix Martínez-Giménez and Alfredo Peris in 2003. We also prove that the tensor product of an operator satisfying the Frequent Hypercyclicity Criterion with the identity is frequently hypercyclic, thereby strengthening a previous result of Martínez-Giménez and Peris.