Dynamics of multivalued linear operators

Abstract

© 2017 Chen et al., 2017. 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.