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Let $G$ be a locally compact group, and let $\pi:G\to\mathcal{C}(V)$ be a strongly continuous representation on a topological vector space $V$ (here $\mathcal{C}(V)$ is the algebra of continuous operators with the strong operator topology).

Question: Has this setup been developed in the literature for categories of $V$ other than Hilbert or Banach spaces? Maybe locally convex, or more general Hausdorff topological spaces?

Precise references would be appreciated. Thank you.

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