Disjoint topological transitivity for cosine operator functions on weighted Orlicz spaces. (English) Zbl 07695404
The author continues in this article the work about dynamics of operators on weighted Orlicz spaces. In the note under review sufficient conditions for sequences of operators to be disjoint topologically transitive on weighted Orlicz spaces of locally compact groups are given. The obtained conditions ensure that the disjoint blow-up/collapse property holds too. Disjoint topological transitivity is a generalization of topological transitivity, which was introduced by L. Bernal-González [Stud. Math. 182, No. 2, 113–131 (2007; Zbl 1134.47006)]. The sequences of operators studied in the article can be regarded as cosine operator functions. It is investigated when they are disjointly topologically mixing. Special cases are considered in the last section.
Reviewer: José Bonet (València)
MSC:
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 47D09 | Operator sine and cosine functions and higher-order Cauchy problems |
| 22D99 | Locally compact groups and their algebras |
Keywords:
disjoint topological transitivity; cosine operator function; weighted Orlicz space; locally compact groupCitations:
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