Let G be a locally compact group. Its dual space, G*, is the set of all extreme points of the set of normalized continuous positive definite functions of G. In the early 1970s, Granirer and Rudin proved independently that if G is amenable as discrete, then G is discrete if and only if all the translation invariant means on are topologically invariant. In this paper, we define and study G*-translation operators on VN(G) via G* and investigate the problem of the existence of G*-translation invariant means on VN(G) which are not topologically invariant. The general properties of G* are also investigated.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-2-1,
author = {Michael Yin-Hei Cheng},
title = {Dual spaces and translation invariant means on group von Neumann algebras},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {97-121},
zbl = {1305.43002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-2-1}
}
Michael Yin-Hei Cheng. Dual spaces and translation invariant means on group von Neumann algebras. Studia Mathematica, Tome 223 (2014) pp. 97-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-2-1/