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arXiv · 1208.2639

Differentiable vectors and unitary representations of Frechet-Lie supergroups

Hadi Salmasian·Karl-Hermann Neeb
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Abstract

For a locally convex Lie group with the Trotter property, we prove that the space of k-times differentiable vectors of a unitary representation is equal to the intersection of domains of k-fold products of the Lie algebra action. The result also holds for continuous representations of locally exponential groups on metrizable locally convex spaces. As an application, we extend a key stability theorem in the representation theory of Lie supergroups beyond the Banach case.

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BibTeXRIS

Hadi Salmasian, Karl-Hermann Neeb. 2012-08-13. Differentiable vectors and unitary representations of Frechet-Lie supergroups. https://arxiv.org/abs/1208.2639

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