Irreducible strongly continuous representations of SL(2,R) on certain Banach spaces are admissible, with admissibility intimately related to the invariant subspace problem.
Warner, Harmonic Analysis on Semi-simple Lie Groups
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Harish-Chandra's admissibility problem for Banach space representations of $\mathrm{SL}(2,\mathbb{R})$
Irreducible strongly continuous representations of SL(2,R) on certain Banach spaces are admissible, with admissibility intimately related to the invariant subspace problem.