Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_{i};=;Y_{i}$, for i = 1,2,...,n. In this article, we showed the following: Let H be a Hilbert space and let L be a subspace lattice on H. Let X and Y be operators acting on H. Assume that range(X) is dense in H. Then the following statements are equivalent: (1) There exists an operator A in AlgL such that AX = Y, $A^{*}$ = A and every E in L reduces A. (2) sup ${frac{$mid$$mid${sum_{i=1}}^n;E_iYf_i$mid$$mid$}{$mid$$mid${sum_{i=1}}^n;E_iXf_i$mid$$mid$}$</TEX>:n{epsilon}N,f_i{epsilon}H;and;E_i{epsilon}L};<;{infty}$</TEX> and <EY f, Xg> = <EX f, Yg> for all E in L and all f, g in H.