Harish-Chandra's admissibility problem for Banach space representations of $\mathrm{SL}(2,\mathbb{R})$

Abstract

We show that irreducible strongly continuous representations of $\mathrm{SL}(2,\mathbb{R})$ on certain Banach spaces are admissible and that the admissibility of Banach space representations of SL(2,R) and the invariant subspace problem are intimately related.