AUT Journal of Mathematics and Computing

AUT Journal of Mathematics and Computing

Quasi-multipliers and quasi Jordan multipliers

Document Type : Original Article

Author
Abbas Zivari-Kazempour
Department of Mathematics, Faculty of Basic Science, Ayatollah Boroujerdi University, Boroujerd, Iran
10.22060/ajmc.2025.23476.1260
Abstract
We show that every quasi-multiplier $‎\phi‎‎:‎L^1(G)‎\times ‎L^1(G)‎‎\longrightarrow ‎L^1(G)‎$, ‎where‎‎‎ ‎‎$‎G‎$ is a locally compact group, is of the form ‎‎‎‎$$‎‎‎‎‎‎‎‎‎‎‎\phi(f,g)=f‎\star ‎‎\mu‎\star ‎‎g‎,\ \ \ \ \ f,g\in ‎L^1(G),‎$$ for a unique measure ‎‎$‎\mu\in ‎‎‎‎M(G)‎$. ‎‎‎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 ‎$‎L^1(G)‎$‎, is a quasi-multiplier.
Keywords
Quasi multiplier
Quasi Jordan multiplier&lrm
&lrm
Separating point&lrm
Group algebra
C^*&lrm
$&lrm
-algebra
Subjects
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AUT Journal of Mathematics and Computing
Volume 7, Issue 2
2026
Pages 175-181