What question did this study set out to answer?

The study aims to identify the normalizer of S(G) within R(G) and its relation to class functions on G.

March 29, 2026Open Access

Commuting Operators and Class Functions

Key Points

The study aims to identify the normalizer of S(G) within R(G) and its relation to class functions on G.
Defined algebras of operators R(G) and S(G) based on group translations and multiplication
Followed the group-measure construction methodology of von Neumann algebras
Examined the normalizer of S(G) in R(G)
Identified the normalizer of S(G) in R(G) with the space of class functions on G
Demonstrated connections between operator algebras and class functions

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 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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