Abstract:
A complete description of all topological groups admitting a separating system of continuous irreducible finite-dimensional unitary representations of uniformly bounded dimensions is obtained. A similar description is obtained for the formally more general class of all unitarily representable topological groups whose von Neumann algebra is a sum of homogeneous summands of finite and uniformly bounded degrees. Related results are obtained; in particular, a description is given of all locally bounded topological groups all of whose irreducible unitary representations are finite-dimensional.
\Bibitem{Sht05}
\by A.~I.~Shtern
\paper Topological groups with finite von Neumann algebras of type~I
\jour Sb. Math.
\yr 2005
\vol 196
\issue 3
\pages 447--463
\mathnet{http://mi.mathnet.ru/eng/sm1279}
\crossref{https://doi.org/10.1070/SM2005v196n03ABEH000887}
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Linking options:
https://www.mathnet.ru/eng/sm1279
https://doi.org/10.1070/SM2005v196n03ABEH000887
https://www.mathnet.ru/eng/sm/v196/i3/p143
This publication is cited in the following 6 articles:
A. I. Shtern, “The structure of homomorphisms of connected locally compact groups into compact groups”, Izv. Math., 75:6 (2011), 1279–1304
A. I. Shtern, “Duality between compactness and discreteness beyond Pontryagin duality”, Proc. Steklov Inst. Math., 271 (2010), 212–227
Shtern A.I., “A criterion for a topological group to admit a continuous embedding in a locally compact group”, Russ. J. Math. Phys., 15:2 (2008), 297–300
Shtern A.I., “Fourier-Stieltjes localization in neighborhoods of finite-dimensional irreducible representations of locally compact groups”, Russ. J. Math. Phys., 13:4 (2006), 458–465
A. I. Shtern, “Weak and strong continuity of representations of topologically pseudocomplete groups in locally convex spaces”, Sb. Math., 197:3 (2006), 453–473
A. I. Shtern, “Almost periodic functions and representations in locally convex spaces”, Russian Math. Surveys, 60:3 (2005), 489–557
Citation in format AMSBIB
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