Mixing properties for nonautonomous linear dynamics and invariant sets

We study mixing properties (topological mixing and weak mixing of arbitrary order) for nonautonomous linear dynamical systems that are induced by the corresponding dynamics on certain invariant sets. The kinds of nonautonomous systems considered here can be defined using a sequence (Ti)i∈N(Ti)i∈N of linear operators Ti:X→XTi:X→X on a topological vector space XX such that there is an invariant set YY for which the dynamics restricted to YY satisfies a certain mixing property. We then obtain the corresponding mixing property on the closed linear span of YY. We also prove that the class of nonautonomous linear dynamical systems that are weakly mixing of order nn contains strictly the corresponding class with the weak mixing property of order n+1n+1.