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

  Published:2017-06-20
 Printed: Jun 2017
  • N. Shravan Kumar,
    Department of Mathematics, Indian Institute of Technology Delhi, Delhi-110016, India
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Abstract

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.
Keywords: ultraspherical hypergroup, Fourier algebra, Fourier-Stieltjes algebra, invariant mean, generalized translation, generalized invariant mean ultraspherical hypergroup, Fourier algebra, Fourier-Stieltjes algebra, invariant mean, generalized translation, generalized invariant mean
MSC Classifications: 43A62, 46J10, 43A30, 20N20 show english descriptions Hypergroups
Banach algebras of continuous functions, function algebras [See also 46E25]
Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Hypergroups
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
 

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