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Unitary representations of locally compact groups as metric structures
For a locally compact group $G$, we show that it is possible to present the class of continuous unitary representations of $G$ as an elementary class of metric structures, in the sense of continuous logic. More precisely, we show how non-degenerate $*$-representations of a general $*$-algebra $A$ (with some mild assumptions) can be viewed as an elementary class, in a many-sorted language, and use the correspondence between continuous unitary representations of $G$ and non-degeneratedoi:10.48550/arxiv.2111.02835 fatcat:a5digkkwffbjpgl4r6xtvshgri