Invariant means on a class of von Neumann algebras
related to ultraspherical hypergroups
Studia Mathematica, Tome 225 (2014) no. 3, pp. 235-247
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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, invariant means on VN$(K)$ are defined and studied. We show that the set of invariant means on VN$(K)$ is nonempty. Also, we prove that, if $H$ is an open subhypergroup of $K,$ then the number of invariant means on VN$(H)$ is equal to the number of invariant means on VN$(K).$ We also show that a unique topological invariant mean exists precisely when $K$ is discrete. Finally, we show that the set TIM$(\widehat{K})$ becomes uncountable if $K$ is nondiscrete.
Keywords:
ultraspherical hypergroup associated locally compact group spherical projector denote dual fourier algebra corresponding note invariant means defined studied set invariant means nonempty prove subhypergroup number invariant means equal number invariant means unique topological invariant mean exists precisely discrete finally set tim widehat becomes uncountable nondiscrete
Affiliations des auteurs :
Nageswaran Shravan Kumar 1
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author = {Nageswaran Shravan Kumar},
title = {Invariant means on a class of von {Neumann} algebras
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journal = {Studia Mathematica},
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volume = {225},
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Nageswaran Shravan Kumar. Invariant means on a class of von Neumann algebras related to ultraspherical hypergroups. Studia Mathematica, Tome 225 (2014) no. 3, pp. 235-247. doi: 10.4064/sm225-3-4
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