Functions of perturbed pairs of noncommuting contractions

Abstract

We consider functions of pairs of noncommuting contractions on Hilbert space and study the problem as to which functions we have Lipschitz type estimates in Schatten–von Neumann norms. We prove that if belongs to the Besov class of analytic functions in the bidisc, then we have a Lipschitz type estimate for functions of pairs of not necessarily commuting contractions in the Schatten–von Neumann norms for . On the other hand, we show that for functions in , there are no such Lipschitz type estimates for , nor in the operator norm.