We present a new approach to determining supports of extreme, normed by 1, positive definite class functions of discrete groups, i.e. characters in the sense of E. Thoma [8]. Any character of a group produces a unitary representation and thus a von Neumann algebra of linear operators with finite normal trace. We use a theorem of H. Umegaki [9] on the uniqueness of conditional expectation in finite von Neumann algebras. Some applications and examples are given.
@article{bwmeta1.element.bwnjournal-article-apmv67z2p199bwm,
author = {Ernest P\l onka},
title = {On a method of determining supports of Thoma's characters of discrete groups},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {199-202},
zbl = {0882.43007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z2p199bwm}
}
Ernest Płonka. On a method of determining supports of Thoma's characters of discrete groups. Annales Polonici Mathematici, Tome 66 (1997) pp. 199-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z2p199bwm/
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