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Paper IPM / M / 17150  


Abstract:  
Let $H$ be an ultraspherical hypergroup and let $A(H)$ be the Fourier algebra associated with $H.$ In this paper we study the dual and the double dual of $A(H).$ We prove among other things that the subspace of all uniformly continuous functionals on $A(H)$ forms a $C^*$algebra. We also prove that the double dual $A(H)^{\ast\ast}$ is neither commutative nor semisimple w.r.t. the Arens product, unless the underlying hypergroup $H$ is finite. Finally, we study the unit elements of $A(H)^{\ast\ast}.$
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