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Mat. Zametki, 2008, Volume 84, Issue 2, Pages 219–230 (Mi mz4025)  

On Almost Representations of Groups with Property (T)

V. M. Manuilova, Yu. Chaob

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Harbin Institute of Technology

Abstract: Kazhdan's property (T) for groups is equivalent to the alternative that a representation of such a group either has an invariant vector or does not have even almost invariant vectors. It is shown that, under a somewhat stronger condition due to Żuk, a similar alternative holds for almost representations.

Keywords: group representation, almost representation, Żuk's condition, Kazhdan's property (T) for groups, Kazhdan constant, group $C^*$-algebra, Hilbert space, linear operator

DOI: https://doi.org/10.4213/mzm4025

Full text: PDF file (494 kB)
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English version:
Mathematical Notes, 2008, 84:2, 207–217

Bibliographic databases:

UDC: 517.98
Received: 14.08.2007

Citation: V. M. Manuilov, Yu. Chao, “On Almost Representations of Groups with Property (T)”, Mat. Zametki, 84:2 (2008), 219–230; Math. Notes, 84:2 (2008), 207–217

Citation in format AMSBIB
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