Abstract
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 Fr\'echet representations of moderate growth) whose module of finite vectors is Harish-Chandra. As an application, we extend to Lie supergroups a general general form of the Gel'fand-Kazhdan criterion due to Sun-Zhu.
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