Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions

In this paper we prove that for an arbitrary pair {T1, T0} of contractions on Hilbert space with trace class difference, there exists a function ξ in L1(T) (called a spectral shift function for the pair {T1, T0}) such that the trace formula trace(f(T1) − f(T0)) = ∫Tfdζ holds for an arbitrary operator Lipschitz function f analytic in the unit disk. © 2017, Springer Science+Business Media, LLC.