Amenability of the Second Dual of Hypergroup Algebras |
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Authors: | A R Medghalchi S M S Modarres |
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Institution: | (1) Institute of Mathematics, University for Teacher Education, 599 Taleghani Avenue, Tehran, 15614, Iran |
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Abstract: | The amenability of the Banach algebra L
1(G), the measure algebra M(G) and their second duals of a locally compact group have been considered by a number of authors. During these investigations it has been shown that L
1(G)** is amenable if and only if G is finite. If LUC (G)*, the dual of the space of left uniformly continuous functions on G, is amenable, then G is compact and M(G) is amenable. Finally, if M(G)** is amenable, then G is finite. The aim of this paper is to generalize all of the above results to the locally compact hypergroups. |
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