Let W(z) be a power series with operator coefficients such that multiplication by W(z) is contractive in C(z). The overlapping space $L(varphi)$ of H(W) in C(z) is a Herglotz space with Herglotz function $varphi(z)$ which satisfies $varphi(z)+varphi^＊(z^{-1})=2[1-W^{*}(z^{-1})W(z)]$. The identity ${}_{L(varphi)}={-}_{H(W)}$ holds for every f(z) in $L(varphi)$ and for every vector c.