Annals of Functional Analysis

Stability results for $C^*$-unitarizable groups

Rachid El Harti and Paulo R. Pinto

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‎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.

Article information

Ann. Funct. Anal., Volume 2, Number 2 (2011), 1- 9.

First available in Project Euclid: 12 May 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L07‎ ‎43A07‎ ‎43A65

Unitarizable representation ‎group $C^*$-algebra ‎similarity problem ‎amenable group


El Harti, Rachid; Pinto, Paulo R. Stability results for $C^*$-unitarizable groups. Ann. Funct. Anal. 2 (2011), no. 2, 1-- 9. doi:10.15352/afa/1399900189.

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