Topological dynamics on weighted solid spaces

Abstract

In this paper, we characterize disjoint supercyclic weighted composition operators on a large class of solid Banach function spaces, with applications to weighted translations on Morrey spaces, and we provide concrete examples. Further, we study the dynamics of cosine operator functions generated by weighted composition operators on solid Banach function spaces, in particular on Orlicz and Morrey spaces, and we give sufficient conditions for supercyclicity of such cosine operator functions in terms of the corresponding weight function. Also, we give concrete examples of weighted translations satisfying these sufficient conditions. Finally, we characterize disjoint topologically transitive weighted composition operators on weighted solid Banach function spaces and we apply our result to the case of translations on weighted Morrey spaces.