This work shows the structure of quasi-multipliers in locally compact groups and $C^$-algebras, indicating important relationships in functional analysis.
We show that every quasi-multiplier φ:L¹(G)× L¹(G) L¹(G), where $G$ is a locally compact group, is of the form φ(f,g)=f μ g,\ \ \ \ \ f,g∈ L¹(G), for a unique measure μ∈ M(G). As a consequence, we obtain a well-known result due to Wendel. We also prove the analogues result for C^*-algebras. Moreover, we introduce the notion of quasi Jordan multipliers and prove that each such map on a C^*-algebra, as well as group algebra L¹(G), is a quasi-multiplier.
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Abbas Zivari-Kazempour (2026) studied this question.
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