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.

15 pages, extensively revised to focus on general Banach spaces rather than on Hilbert spaces