On a method of determining supports of Thoma's characters of discrete groups

Volume 67 / 1997

Ernest Płonka Annales Polonici Mathematici 67 (1997), 199-202 DOI: 10.4064/ap-67-2-199-202


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.


  • Ernest Płonka

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