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Proceedings of the YSU, Physical and Mathematial Scineces, 2010, Issue 3, Pages 40–43 (Mi uzeru223)  

Mathematics

Non-unitarizable groups

H. R. Rostami

Chair of Algebra and Geometry YSU, Armenia

Abstract: A group $G$ is called unitarizable, if every uniformly bounded representation $\pi:G\to B(H)$ of $G$ on a Hilbert space $H$ is unitarizable. N. Monod and N. Ozawa in [6] prove that free Burnside groups $B(m,n)$ are non unitarizable for arbitrary composite odd number $n=n_1n_2$, where $n_\geq665$. We prove that for the same $n$ the groups $B(4,n)$ have continuum many non-isomorphic factor-groups, each one of which is non-unitarizable and uniformly non-amenable.

Keywords: representation of group, unitarizable group, free Burnside group, periodic group.

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Received: 05.09.2009
Accepted:15.10.2009
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Citation: H. R. Rostami, “Non-unitarizable groups”, Proceedings of the YSU, Physical and Mathematial Scineces, 2010, no. 3, 40–43

Citation in format AMSBIB
\Bibitem{Ros10}
\by H.~R.~Rostami
\paper Non-unitarizable groups
\jour Proceedings of the YSU, Physical and Mathematial Scineces
\yr 2010
\issue 3
\pages 40--43
\mathnet{http://mi.mathnet.ru/uzeru223}


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