The computation of the H-infinity optimal weighted pure and mixed sensitivities for a class of infinite-dimensional systems is studied by characterizing certain wandering subspaces of some related Krein spaces. The new characterizations can de used to obtain explicit bases for those subspaces. Explicit formulas for the optimal sensitivity for some infinite-dimensional systems can be obtained from these bases. The new characterizations can also be used to obtain fast algorithms for computing the H-infinity optimal performance for pure and mixed sensitivity problems. The results are applied to obtain an explicit optimal sensitivity formula for a class of infinite-dimensional systems that generalizes a known result.