Abstract
Let U be a continuous representation of a (connected) locally compact group G in a separated locally convex space E. It is shown that the study of U is equivalent to the study of a family U i of continuous representations of G in Fréchet spaces F i. If U is equicontinuous, the F i are Banach spaces, and the U i are realized by isometric operators. When U is topologically irreducible, it is Naïmark equivalent to a Fréchet (or isometric Banach, in the equicontinuous case) continuous representation. Similar results hold for semi-groups.
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Jurzak, J.P. A contribution to group representations in locally convex spaces. Lett Math Phys 1, 513–519 (1977). https://doi.org/10.1007/BF00399744
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DOI: https://doi.org/10.1007/BF00399744