Characterization of Operators on the Dual of Hypergroups which Commute with Translations and Convolutions

作     者：Ali Ghaffari Alireza Medghalchi 

作者机构：Department of MathematicsSemnan UniversityP.O.Box 35195-363SemnanIran Department of MathematicsTeacher Training UniversityTehranIran. 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2004年第20卷第2期

页      面：201-208页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Hypergroup algebras Group algebras Operators Translations Convolutions Invariant 

摘      要：For a locally compact group G, L 1(G) is its group algebra and L ∞(G) is the dual of L 1(G). Lau has studied the bounded linear operators T : L ∞(G) → L ∞(G) which commute with convolutions and translations. For a subspace H of L ∞(G), we know that M(L ∞(G),H), the Banach algebra of all bounded linear operators on L ∞(G) into H which commute with convolutions, has been studied by Pym and Lau. In this paper, we generalize these problems to L(K)*, the dual of a hypergroup algebra L(K) in a very general setting, i. e. we do not assume that K admits a Haar measure. It should be noted that these algebras include not only the group algebra L 1(G) but also most of the semigroup algebras. Compact hypergroups have a Haar measure, however, in general it is not known that every hypergroup has a Haar measure. The lack of the Haar measure and involution presents many difficulties; however, we succeed in getting some interesting results.