Abstract
Let K be a commutative or compact hypergroup. Let \(\mu \) be a bounded complex-valued Borel measure on K, and let \(T_\mu \) be the corresponding convolution operator of \(L^1(K)\). Let S be a bounded linear operator on a Banach space X. We prove that every linear operator \(\Psi : X \rightarrow L^1(K)\) such that \(\Psi S=T_\mu \Psi \) is continuous if and only if the pair \((S,T_\mu )\) has no critical eigenvalues.
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Acknowledgements
The authors thank the reviewer for his/her valuable comments/suggestions. Vishvesh Kumar is supported by FWO Odysseus 1 Grant G.0H94.18N: Analysis and Partial Differential Equations.
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Kumar, V., Sarma, R. Continuity of operators intertwining with translation operators on hypergroups. Aequat. Math. 95, 343–349 (2021). https://doi.org/10.1007/s00010-020-00745-y
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DOI: https://doi.org/10.1007/s00010-020-00745-y