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Invariant Means on a Class of von Neumann Algebras Related to Ultraspherical Hypergroups II
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- Journal:
- Canadian Mathematical Bulletin / Volume 60 / Issue 2 / 01 June 2017
- Published online by Cambridge University Press:
- 20 November 2018, pp. 402-410
- Print publication:
- 01 June 2017
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- Article
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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.
