On F-semi-transitive families of operators

Abstract

Motivated by the concept of topological transitivity for supercyclicity, in this paper, we present the concept of Furstenberg-semi-transitivity. Then we provide sufficient conditions for cosine operator functions generated by the adjoints of weighted composition operators to be Furstenberg-semi-transitive on the space of Radon measures on a locally compact, non-compact Hausdorff space. Also, we characterize disjoint Furstenberg-semi-transitive compositions of a right multiplier and a generalized weighted bilateral shift on the standard Hilbert module over the C*-algebra of compact operators on a separable Hilbert space. As a special case, we consider the case when the corresponding Furstenberg family is the family of all infinite subsets of the set of natural numbers. Finally, we illustrate our results with concrete examples.