Abstract
We give some sufficient and necessary conditions for translation operators on the weighted Orlicz spaces to be disjoint topologically transitive and disjoint topologically mixing. In particular, we show that in certain cases, operators are disjoint topologically transitive if, and only if, their direct sum is topologically transitive.
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Acknowledgements
The authors thank anonymous reviewers for careful reading of the manuscript and pointing out some important observations (Remark 2.2 and Corollary 3.4) and open questions (Remarks 2.5, 3.7) that improved this paper a lot. Funding was provided by Ministry of Science and Technology, Taiwan (Grant No. MOST 109-2115-M-142-002).
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Communicated by H. Turgay Kaptanoglu.
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This article is part of the topical collection “Harmonic Analysis and Operator Theory” edited by H. Turgay Kaptanoglu, Aurelian Gheondea and Serap Oztop.
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Chen, CC., Öztop, S. & Tabatabaie, S.M. Disjoint Dynamics on Weighted Orlicz Spaces. Complex Anal. Oper. Theory 14, 72 (2020). https://doi.org/10.1007/s11785-020-01034-x
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DOI: https://doi.org/10.1007/s11785-020-01034-x