Stability Results for C∗-unitarizable Groups

We say that a locally compact group G is C∗-unitarizable if its full group C∗-algebra C∗(G) satisfies Kadison’s similarity problem (SP), i.e. every bounded representation of C∗(G) on a Hilbert space is similar to a *representation. We prove that locally compact and unitarizable groups are C∗-unitarizable. For discrete groups, we prove that C∗-unitarizable passes to quotients. Moreover, a given discrete group is C∗-unitarizable whenever we can find a normal and C∗-unitarizable subgroup with amenable quotient. 1 Department of Mathematics and Computer Sciences, Faculty of Sciences and Techniques, University Hassan I, BP 577. 26000 Settat, Morocco. E-mail address: [email protected] 2 Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal. E-mail address: [email protected] Date: Received: 11 January 2011; Accepted: 30 May 2011. ∗ Corresponding author. 2010 Mathematics Subject Classification. Primary 46L05; Secondary 46L07, 43A07, 43A65.