Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

Streszczenie

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, invariant means on VN$(K)$ are defined and studied. We show that the set of invariant means on VN$(K)$ is nonempty. Also, we prove that, if $H$ is an open subhypergroup of $K,$ then the number of invariant means on VN$(H)$ is equal to the number of invariant means on VN$(K).$ We also show that a unique topological invariant mean exists precisely when $K$ is discrete. Finally, we show that the set TIM$(\widehat{K})$ becomes uncountable if $K$ is nondiscrete.