Abstract
Let G be a locally compact totally disconnected topological group. Under a necessary mild assumption, we show that the irreducible unitary representations of G are uniformly admissible if and only if the irreducible smooth representations of G are uniformly admissible. An analogous result for *-algebras is also established. We further show that the property of having uniformly admissible irreducible smooth representations is inherited by finite-index subgroups and overgroups of G.
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Acknowledgements
We thank Maarten Solleveld for encouraging us to publish this note and the anonymous referee for suggesting to include Theorem 2.6.
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First, U.A., Rüd, T. On uniform admissibility of unitary and smooth representations. Arch. Math. 112, 169–179 (2019). https://doi.org/10.1007/s00013-018-1257-y
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DOI: https://doi.org/10.1007/s00013-018-1257-y