Invariant Means on a Class of von Neumann Algebras Related to Ultraspherical Hypergroups II
Printed: Jun 2017
Let $K$ be an ultraspherical hypergroup associated to a locally
compact group $G$ and a spherical projector $\pi$ and let $VN(K)$
denote the dual of the Fourier algebra $A(K)$ corresponding to
$K.$ In this note, we show that the set of invariant means on
$VN(K)$ 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.
ultraspherical hypergroup, Fourier algebra, Fourier-Stieltjes algebra, invariant mean, generalized translation, generalized invariant mean
43A62 - Hypergroups
46J10 - Banach algebras of continuous functions, function algebras [See also 46E25]
43A30 - Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
20N20 - Hypergroups