The Distance to Intertwining Operators, Contractive Liftings and a Related Optimality Result

Given the distance of a contraction A to the kernel of a intertwining relation we estimate the minimal distance of contractive liftings of A to the kernel of the lifted intertwining relation. We also present a related optimality result which involves the inequality ||F|l<=||F(lambda) *||, where F and * are given operators and (lambda)is an arbitrary comple* number.