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 is coamenable if and only if the contra-corepresentation of its fundamental multiplicative unitary is Bekka-amenable, and that is amenable if and only if its dual quantum group’s fundamental multiplicative unitary is weakly Bekka-amenable.
"Bekka-type amenabilities for unitary corepresentations of locally compact quantum groups." Ann. Funct. Anal. 9 (2) 210 - 219, May 2018. https://doi.org/10.1215/20088752-2017-0044