Published online by Cambridge University Press: 20 November 2018
Let $K$ be an ultraspherical hypergroup associated with a locally compact group
$G$ and a spherical projector
$\pi$ and let
$\text{VN}(K)$ denote the dual of the Fourier algebra
$A(K)$ corresponding to
$K$. In this note, we show that the set of invariant means on
$\text{VN}(K)$ is singleton if and only if
$K$ is discrete. Here
$K$ need not be second countable. We also study invariant means on the dual of the Fourier algebra
${{A}_{0}}(K)$, the closure of
$A(K)$ in the cb-multiplier norm. Finally, we consider generalized translations and generalized invariant means.