The factorization problem for nonnegative operator valued functions

Abstract

Introduction. Let f be a function defined on the circle T = {e ie : 0 ^ 6 < 2T } or line R = ( -<*>, <*> ) whose values are nonnegative operators on a separable complex Hubert space. We are concerned with the problem of finding conditions that F = G*G a.e. where G is the strong boundary value function of a suitable operator valued analytic function defined in the disk \z\ <1 or half-plane y>0. Mainly we are interested in special classes of functions in which such a factorization is always possible.