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Paper   IPM / M / 17150
School of Mathematics
  Title:   On the algebras $Vn(H)$ and $Vn(H)^{*}$ of an ultraspherical hypergroup $H$
  Author(s):  Mehdi Nemati (Joint with R. Esmailvandi and N. Shravan Kumar)
  Status:   To Appear
  Journal: J. Aust. Math. Soc.
  Supported by:  IPM
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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