location:  Publications → journals → CMB
Abstract view

# 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
 Format: LaTeX MathJax PDF

## 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
 MSC Classifications: 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

 top of page | contact us | privacy | site map |