Geodesic
Noncommutative Riesz Theorem and Weak Burnside Type Theorem on Twisted Conjugacy
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 2, pp. 44-54.

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The paper consists of two parts. In the first part, we prove a noncommutative analog of the Riesz(–Markov–Kakutani) theorem on representation of functionals on an algebra of continuous functions by regular measures on the underlying space. In the second part, using this result, we prove a weak version of a Burnside type theorem on twisted conjugacy for arbitrary discrete groups. 
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E. V. Troitskii. Noncommutative Riesz Theorem and Weak Burnside Type Theorem on Twisted Conjugacy. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 2, pp. 44-54. http://geodesic.mathdoc.fr/item/FAA_2006_40_2_a4/

[1] Diksme Zh., $C^*$-algebry i ikh predstavleniya, Mir, M., 1974

[2] Kirillov A. A., Elementy teorii predstavlenii, Nauka, M., 1978 | MR | Zbl

[3] Merfi A., $C^*$-algebry i teoriya operatorov, Faktorial Press, M., 1997

[4] Felshtyn A. L., “Chislo Raidemaistera lyubogo avtomorfizma giperbolicheskoi po Gromovu gruppy beskonechno”, Geom. i topol. 6, Zap. nauchn. sem. POMI, 279, 2001, 229–240, 250 | MR

[5] Arthur J., Clozel L., Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula, Princeton University Press, Princeton, NJ, 1989 | MR | Zbl

[6] Dauns J., Hofmann K. H., Representations of rings by continuous sections, Mem. Amer. Math. Soc., 83, Amer. Math. Soc., Providence, RI, 1968 | MR

[7] Fell J. M. G., “The structure of algebras of operator fields”, Acta Math., 106 (1961), 233–280 | DOI | MR | Zbl

[8] Fel'shtyn A., Dynamical zeta functions, Nielsen theory and Reidemeister torsion, Mem. Amer. Math. Soc., 147, No. 699, 2000 | MR

[9] Fel'shtyn A., Troitsky E., “A twisted Burnside theorem for countable groups and Reidemeister numbers”, Proc. Workshop Noncommutative Geometry and Number Theory (Bonn, 2003), eds. Consani K., Marcolli M., Manin Yu., Vieweg, Braunschweig, 2006, 141–154 ; Preprint MPIM2004-65 | DOI | MR

[10] Fel'shtyn A., Troitsky E., Vershik A., Twisted Burnside theorem for type II${}_1$ groups: an example, Preprint 85, Max-Planck-Institut für Mathematik, 2004 | MR

[11] Grothendieck A., “Formules de Nielsen-Wecken et de Lefschetz en géométrie algébrique”, Séminaire de Géométrie Algébrique du Bois-Marie 1965–66. SGA 5, Lecture Notes in Math., 569, Springer-Verlag, Berlin, 1977, 407–441 | DOI | MR

[12] Jiang B., Lectures on Nielsen Fixed Point Theory, Contemp. Math., 14, Amer. Math. Soc., Providence, RI, 1983 | DOI | MR

[13] Pedersen G. K., $C^*$-Algebras and Their Automorphism Groups, Academic Press, London–New York–San Francisco, 1979 | MR | Zbl

[14] Shokranian S., The Selberg–Arthur Trace Formula, Based on lectures by James Arthur, Springer-Verlag, Berlin, 1992 | MR | Zbl