Double operator integrals and operator Lipschitz estimates

Abstract: 

Nearly half a century ago M.G. Krein made an elusive conjecture on the behaviour of operator-valued Lipschitz functions. It was only very recently that a resolution to his conjecture was found in the self-adjoint setting by applying the theory of double operator integrals. In this talk we will firstly try to understand why the double operator integral is such an important tool in perturbation theory, and then move to discuss a translation of Krein's original conjecture to the unitary setting along with a solution to this new problem.