Abstract
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 with respect to the Arens product, unless the underlying hypergroup H is finite. Finally, we study the unit elements of
$A(H)^{\ast \ast }.$
Publisher
Cambridge University Press (CUP)