Sufficiently close one-dimensional pseudorepresentations are equal (Q2037785)

In this interesting short paper, the author gives a sufficient condition such that two one-dimensional pseudorepresentations of a group coincide. This result does not hold for pseudorepresentations whose dimension is greater than one. Finally the following is shown: Let \(\pi\) and \(\rho\) be bounded pseudorepresentations of a group \(G\) into finite-dimensional Banach spaces \(E\) and \(F\). If the characters \(\chi_\pi\) and \(\chi_\rho\) of \(\pi\) and \(\rho\), respectively, coincide, then \(\pi\) and \(\rho\) are pointwise equivalent.