Quasi-multipliers and quasi Jordan multipliers

Articles in Press

Document Type : Original Article

Author

Department of Mathematics, Faculty of Basic Science, Ayatollah Boroujerdi University, Boroujerd, Iran

Abstract

We show that every quasi-multiplier

‎ ϕ ‎ ‎ : ‎ L^{1} (G) ‎ \times ‎ L^{1} (G) ‎ ‎ ⟶ ‎ L^{1} (G) ‎

, ‎where‎‎‎ ‎‎

‎ G ‎

is a locally compact group, is of the form ‎‎‎‎

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ϕ (f, g) = f ‎ ⋆ ‎ ‎ μ ‎ ⋆ ‎ ‎ g ‎, f, g \in ‎ L^{1} (G), ‎

for a unique measure ‎‎

‎ μ \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

Main Subjects