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Noncommutative Riesz theorem and weak Burnside type theorem on twisted conjugacy

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Abstract

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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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 40, No. 2, pp. 44–54, 2006

Original Russian Text Copyright © by E. V. Troitsky

Supported in part by the RFBR (grant No. 05-01-00923), the program “Support of Leading Scientific Schools” (grant No. NSh-619.2003.1) and the program “Universities of Russia” (grant No. UR.04.02.530).

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Troitsky, E.V. Noncommutative Riesz theorem and weak Burnside type theorem on twisted conjugacy. Funct Anal Its Appl 40, 117–125 (2006). https://doi.org/10.1007/s10688-006-0018-z

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  • DOI: https://doi.org/10.1007/s10688-006-0018-z

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