Roughness and approximation of quasi-representations of amenable groups

Sufficient conditions are obrained for a quasi-representation (not necessarily bounded) of an amenable group (topological in general) to be a bounded perturbation of an ordinary representation. In particular, it is shown that an arbitrary (not necessarily bounded) finite-dimensional quasi-representation of an amenable topological group is a bounded perturbation of an ordinary representation. Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 908–920, June, 1999.