Frechet Globalisations of Harish-Chandra Supermodules

For any Lie supergroup whose underlying Lie group is reductive, we prove an extension of the Casselman-Wallach globalisation theorem: there is an equivalence between the category of Harish-Chandra modules and the category of SF-representations (smooth Frechet representations of moderate growth) whose module of finite vectors is Harish-Chandra. As an application, we extend to Lie supergroups a general form of the Gelfand-Kazhdan criterion due to Sun-Zhu