Lower upper factorizations of operators with middle terms

AbstractIn this paper we consider factorizations of the form I − K = (I + K−)(D + F)(I + K+), where K−, K+, and D are lower, upper, and diagonal operators relative to a maximal chain P of orthoprojections in a separable Hilbert space.In the case when K, K−, and K+ are Hilbert-Schmidt, we determine the minimal rank of the operator F which occurs in the middle term of the factorization