On the differentiable vectors for contragredient representations

Abstract

We establish a few simple results on contragredient representations of Lie groups, with a view toward applications to the abstract characterization of some spaces of pseudo-differential operators. In particular, this method provides an abstract approach to J.Nourrigat's recent description of the norm closure of the pseudo-differential operators of order zero.

6 pages; the final version is published in C. R. Math. Acad. Sci. Paris 351 (2013), no. 13-14, 513--516