## Annals of Functional Analysis

### Bekka-type amenabilities for unitary corepresentations of locally compact quantum groups

Xiao Chen

#### Abstract

In this short note, we further Ng’s work by extending Bekka amenability and weak Bekka amenability to general locally compact quantum groups, and we generalize some of Ng’s results to the general case. In particular, we show that a locally compact quantum group ${\mathbb{G}}$ is coamenable if and only if the contra-corepresentation of its fundamental multiplicative unitary $W_{\mathbb{G}}$ is Bekka-amenable, and that ${\mathbb{G}}$ is amenable if and only if its dual quantum group’s fundamental multiplicative unitary $W_{\widehat{\mathbb{G}}}$ is weakly Bekka-amenable.

#### Article information

Source
Ann. Funct. Anal., Volume 9, Number 2 (2018), 210-219.

Dates
Accepted: 5 May 2017
First available in Project Euclid: 7 December 2017

https://projecteuclid.org/euclid.afa/1512637230

Digital Object Identifier
doi:10.1215/20088752-2017-0044

Mathematical Reviews number (MathSciNet)
MR3795086

Zentralblatt MATH identifier
06873698

#### Citation

Chen, Xiao. Bekka-type amenabilities for unitary corepresentations of locally compact quantum groups. Ann. Funct. Anal. 9 (2018), no. 2, 210--219. doi:10.1215/20088752-2017-0044. https://projecteuclid.org/euclid.afa/1512637230

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