Let K be an ultraspherical hypergroup associated to a locally compact group G and a spherical projector π 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(K̂) becomes uncountable if K is nondiscrete.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-4,
author = {Nageswaran Shravan Kumar},
title = {Invariant means on a class of von Neumann algebras related to ultraspherical hypergroups},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {235-247},
zbl = {1322.43007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-4}
}
Nageswaran Shravan Kumar. Invariant means on a class of von Neumann algebras related to ultraspherical hypergroups. Studia Mathematica, Tome 223 (2014) pp. 235-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-3-4/