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 with respect to 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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关于代数

设H为超球超群，$A(H)$为与$H相关的傅里​​叶代数。$在本文中，我们研究$A(H).$ 的对偶和双对偶。$我们证明了$A(H)$上所有一致连续泛函的子空间形成$C^*$代数。我们还证明了双对偶$A(H)^{\ast \ast }$相对于 Arens 乘积既不是交换律也不是半简单的，除非基础超群H是有限的。最后，我们研究$A(H)^{\ast \ast }.$的单位元素