Quasirepresentations of amenable groups: results, errors, and hopes (Q384385)

Any mapping \(T\) of a given group \(G\) into the group of invertible operators of some Banach space \(B\) for which \(\|T(g_1 g_2)-T(g_1)T(g_2)\|\leq\epsilon\) for any \(g_1, g_2\in G\) and for some \(\epsilon>0\), is called an \(\epsilon\)-quasirepresentation. In the paper under review, the structure of continuous Banach space quasirepresentations of amenable topological groups (which are not necessarily locally compact) is discussed. Together with the corresponding results, errors, ways they reveal and correct some errors, and related hopes.