Let G be a locally compact group, G* be the set of all extreme points of the set of normalized continuous positive definite functions of G, and a(G) be the closed subalgebra generated by G* in B(G). When G is abelian, G* is the set of Dirac measures of the dual group Ĝ, and a(G) can be identified as l¹(Ĝ). We study the properties of a(G), particularly its spectrum and its dual von Neumann algebra.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm202-3-5, author = {Michael Yin-hei Cheng}, title = {Subalgebras generated by extreme points in Fourier-Stieltjes algebras of locally compact groups}, journal = {Studia Mathematica}, volume = {204}, year = {2011}, pages = {289-302}, zbl = {1228.43006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm202-3-5} }
Michael Yin-hei Cheng. Subalgebras generated by extreme points in Fourier-Stieltjes algebras of locally compact groups. Studia Mathematica, Tome 204 (2011) pp. 289-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm202-3-5/