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Published online by Cambridge University Press: 12 December 2022
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
$A(H)^{\ast \ast }.$
Communicated by George Willis