We study actions of discrete groups on Hilbert C*-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a quasi-invariant probability measure which is sufficiently close to being invariant.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-2-4, author = {Ronald G. Douglas and Piotr W. Nowak}, title = {Hilbert C*-modules and amenable actions}, journal = {Studia Mathematica}, volume = {196}, year = {2010}, pages = {185-197}, zbl = {05860441}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-2-4} }
Ronald G. Douglas; Piotr W. Nowak. Hilbert C*-modules and amenable actions. Studia Mathematica, Tome 196 (2010) pp. 185-197. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-2-4/