## Bulletin of the Belgian Mathematical Society - Simon Stevin

- Bull. Belg. Math. Soc. Simon Stevin
- Volume 22, Number 2 (2015), 263-269.

### A new look at the proof of $K$-theoretic amenability for groups acting on trees

#### Abstract

We generalize the construction by Pytlik and Szwarc of uniformly bounded representations for free groups to groups acting on trees. We deduce a new version of the proof (by Alain Valette and the author, 1983) of the fact that locally compact groups acting on trees with amenable stabilizers are amenable in $K$-theory.

#### Article information

**Source**

Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 2 (2015), 263-269.

**Dates**

First available in Project Euclid: 28 May 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1432840862

**Digital Object Identifier**

doi:10.36045/bbms/1432840862

**Mathematical Reviews number (MathSciNet)**

MR3351040

**Zentralblatt MATH identifier**

1327.19010

**Subjects**

Primary: 19K35: Kasparov theory ($KK$-theory) [See also 58J22] 19K99: None of the above, but in this section 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 22D10: Unitary representations of locally compact groups 22D12: Other representations of locally compact groups

**Keywords**

K-theory Operator Algebras Group Representation Theory

#### Citation

Julg, Pierre. A new look at the proof of $K$-theoretic amenability for groups acting on trees. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 2, 263--269. doi:10.36045/bbms/1432840862. https://projecteuclid.org/euclid.bbms/1432840862