Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture (Q847929)

A map \(T\) from a group \(G\) to the algebra \(L(E)\) of bounded operators on a Banach space \(E\) is called a quasirepresentation if there exists \(\varepsilon>0\) such that \(\|(T(gh)-T(g)T(h))x\|\leq\varepsilon\|x\|\) for any \(g,h\in G\), \(x\in E\). A description of the structure of all finite-dimensional, locally bounded quasirepresentations of arbitrary connected Lie groups is given. The paper is nicely written and contains a lot of examples and related results, including a generalization of the van der Waerden theorem on automatic continuity for group representations and the proof of Mishchenko's conjecture on the oscillation of discontinuous representations at the identity element of a group.