Resumen de Finite dimensional approximations of operators related to groups and their applications
In the first part we show a generalization of the effective Luck approximation property. We show that there exists a function that bound the spectral concentration of all matrices that appear as representations from an algebraic operator.
In the second part we answer a question posed by Wolfgang Luck. We show that the von Neumann rank function and the von Neumann rank function twisted with a finite dimensional representation only differ by a factor.
In the last part we show shat in general the Brown measure of an Operator from a group ring can not be approximated using finite quotients. We give an explicit counterexample.
