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

Published online by Cambridge University Press:  20 November 2018

N. Shravan Kumar
N. Shravan Kumar*
Affiliation:
Department of Mathematics, Indian Institute of Technology Delhi, Delhi-110016, India. e-mail: shravankumar@maths.iitd.ac.in
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Abstract

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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.

Keywords

43A6246J1043A3020N20ultraspherical hypergroupFourier algebraFourier-Stieltjes algebrainvariant meangeneralized translationgeneralized invariant mean
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 2 , 01 June 2017 , pp. 402 - 410
Copyright
Copyright © Canadian Mathematical Society 2017

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