In this paper, we study the disjointness of topological transitivity on Orlicz spaces endowed with the Orlicz norm. We first give the characterization for weighted translations to be topologically transitive. Based on this, a sufficient condition and a necessary condition for powers of weighted translations to be disjoint topologically transitive are obtained as well.

Let $G$ be a locally compact group, and let $w$ be a weight on $G$. Let $\varPhi $ be a Young function. We give some characterizations for translation operators to be topologically transitive and chaotic on the weighted Orlicz space $L_w^\varPhi (G)$

We introduce several notions of linear dynamics for multivalued linear operators (MLO’s) between separable Fréchet spaces, such as hypercyclicity, topological transitivity, topologically mixing property, and Devaney chaos. We also consider the case of disjointness, in which any of these properties are simultaneously satisfied by several operators. We revisit some sufficient well-known computable criteria for determining those properties. The analysis of the dynamics of extensions of linear operators to MLO’s is also considered.