Invariant means on a class of von Neumann algebras related to ultraspherical hypergroups

Nageswaran Shravan Kumar. "Invariant means on a class of von Neumann algebras related to ultraspherical hypergroups." Studia Mathematica 225.3 (2014): 235-247. <http://eudml.org/doc/285394>.

@article{NageswaranShravanKumar2014,
abstract = {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.},
author = {Nageswaran Shravan Kumar},
journal = {Studia Mathematica},
keywords = {ultraspherical hypergroups; Fourier algebra; von Neumann algebra; invariant mean},
language = {eng},
number = {3},
pages = {235-247},
title = {Invariant means on a class of von Neumann algebras related to ultraspherical hypergroups},
url = {http://eudml.org/doc/285394},
volume = {225},
year = {2014},
}

TY - JOUR
AU - Nageswaran Shravan Kumar
TI - Invariant means on a class of von Neumann algebras related to ultraspherical hypergroups
JO - Studia Mathematica
PY - 2014
VL - 225
IS - 3
SP - 235
EP - 247
AB - 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.
LA - eng
KW - ultraspherical hypergroups; Fourier algebra; von Neumann algebra; invariant mean
UR - http://eudml.org/doc/285394
ER -