Motivated by the computation of the H-infinity optimal performance and optimal mixed sensitivity for a class of infinite dimensional systems, we consider the explicit computation of the norm and minimal symbols of a class of "Hankel plus Toeplitz" type operators with irrational symbols using Krein space approach. We show how to explicitly compute the norm and parameterize all the minimal symbols. The results are used to obtain a complete solution to the H-infinity optimal mixed sensitivity synthesis problem for a class of infinite dimensional systems : an explicit formula for computing the H-infinity optimal performance and explicit parameterization of all optimal and suboptimal mixed sensitivities. An illustrative example is given.