IPM - Institute for Research in Fundamental Sciences

“School of Mathematics”

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

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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