Amenability of groups - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T00:35:12Z http://mathoverflow.net/feeds/question/44843 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/44843/amenability-of-groups Amenability of groups Kate Juschenko 2010-11-04T16:37:51Z 2011-04-06T19:37:22Z <p>Let $G$ be non-amenable finitely generated group.</p> <p>1) Is it true that there exists a sequence $S(n)$ of sets which generate $G$ and such that </p> <p>$\frac{1}{|S(n)|}||\sum_{g\in S(n)} \lambda(g)||\rightarrow 0$ when $n\rightarrow \infty$.</p> <p>2) The same as (1), but $S(n)$ is finite subset of $G$.</p> <p>Here $\lambda:G\rightarrow B(l^2(G))$ is left regular representation of $G$.</p> <p>Also 1) is reformulation of 2).</p> <p><strong>Edit:</strong> <a href="http://mathoverflow.net/questions/55075/amenability-of-groups-iii" rel="nofollow">here</a> are some discussions on the question.</p>