1 results
ON THE ALGEBRAS
$\boldsymbol {VN(H)}$ AND 
$\boldsymbol {VN(H)^{*}} $ OF AN ULTRASPHERICAL HYPERGROUP 
$\boldsymbol {H}$
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 115 / Issue 3 / December 2023
- Published online by Cambridge University Press:
- 12 December 2022, pp. 337-353
- Print publication:
- December 2023
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- Article
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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 
$A(H)^{\ast \ast }.$
