Dual spaces and translation invariant means on group von Neumann algebras

Michael Yin-Hei Cheng. "Dual spaces and translation invariant means on group von Neumann algebras." Studia Mathematica 223.2 (2014): 97-121. <http://eudml.org/doc/285758>.

@article{MichaelYin2014,
abstract = {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 $L^\{∞\}(G)$ 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.},
author = {Michael Yin-Hei Cheng},
journal = {Studia Mathematica},
keywords = {Fourier algebras; Fourier-Stieltjes algebras; locally compact groups; amenability; approximate identity; translation invariant means; von Neumann algebras},
language = {eng},
number = {2},
pages = {97-121},
title = {Dual spaces and translation invariant means on group von Neumann algebras},
url = {http://eudml.org/doc/285758},
volume = {223},
year = {2014},
}

TY - JOUR
AU - Michael Yin-Hei Cheng
TI - Dual spaces and translation invariant means on group von Neumann algebras
JO - Studia Mathematica
PY - 2014
VL - 223
IS - 2
SP - 97
EP - 121
AB - 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 $L^{∞}(G)$ 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.
LA - eng
KW - Fourier algebras; Fourier-Stieltjes algebras; locally compact groups; amenability; approximate identity; translation invariant means; von Neumann algebras
UR - http://eudml.org/doc/285758
ER -