Abstract
For a Young function \(\phi \) and a locally compact second countable group G, let \(L^\phi (G)\) denote the Orlicz space on G. In this paper, we present a necessary and sufficient condition for the topological transitivity of a sequence of cosine operators \(\{C_n\}_{n=1}^{\infty }:=\{\frac{1}{2}(T^n_{g,w}+S^n_{g,w})\}_{n=1}^{\infty }\), defined on \(L^{\phi }(G)\). We investigate the conditions for a sequence of cosine operators to be topologically mixing. Further, we go on to prove a similar result for the direct sum of a sequence of cosine operators. Finally, we give an example of topologically transitive sequence of cosine operators.
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Acknowledgements
Vishvesh Kumar is supported by FWO Odysseus 1 Grant G.0H94.18N: Analysis and Partial Differential Equations. We thank the referee for useful comments and remarks, which helped to improve the final version of the paper.
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Communicated by Pedro Tradacete.
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Akbarbaglu, I., Azimi, M.R. & Kumar, V. Topologically transitive sequence of cosine operators on Orlicz spaces. Ann. Funct. Anal. 12, 3 (2021). https://doi.org/10.1007/s43034-020-00088-4
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DOI: https://doi.org/10.1007/s43034-020-00088-4
Keywords
- Hypercyclicity
- Topologically transitive
- Topologically mixing
- Weighted translation operator
- Orlicz space
- Locally compact group