In this chapter we give a rigorous derivation of the eld equation recursion method in theabstract theory of composites to two-component composites with isotropic phases. Thismethod is of great interest since it has proven to be a powerful tool in developing sharpbounds for the eective tensor of a composite material. The reason is that the eectivetensor L_* can be interpreted in the general framework of the abstract theory of compositesas the Z-operator on a certain orthogonal Z(2) subspace collection. The base case of therecursion starts with an orthogonal Z(2) subspace collection on a Hilbert space H, the Zproblem,and the associated Y -problem. We provide some new conditions for the solvabilityof both the Z-problem and the associated Y -problem. We also give explicit representations ofthe associated Z-operator and Y -operator and study their analytical properties. An iterationmethod is then developed from a hierarchy of subspace collections and their associatedoperators which leads to a continued fraction representation of the initial effctive tensor L_*.