Invariant Means on a Class of von Neumann Algebras Related to Ultraspherical Hypergroups II

Kumar, N. Shravan

Canadian mathematical bulletin, Tome 60 (2017) no. 2, pp. 402-410

Résumé

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.

Détail

DOI : 10.4153/CMB-2016-081-3

Mots-clés : 43A62, 46J10, 43A30, 20N20, ultraspherical hypergroup, Fourier algebra, Fourier-Stieltjes algebra, invariant mean, generalized translation, generalized invariant mean

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