Journal of Lie Theory, 7(2), 239-243 (1997)

Commuting Operators and Class Functions

E. N. Reyes

Southeastern Louisiana University
Hammond, Louisiana, U.S.A. 70402
Abstract: Given a unimodular locally compact group $G$, we associate two algebras of operators, $R(G)$ and $S(G)$. Operators in $R(G)$ are multiplication operators and those in $S(G)$ are defined by group translations on $G\times G$. The construction of these algebras follow closely the so-called `group-measure' construction of von Neumann algebras due to Murray and von Neumann. In this paper, we show that the `normalizer' (a study began by Judith Packer) of $S(G)$ in $R(G)$ is identified with the space of class functions on $G$.

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