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 L, be a subspace lattice on a Hilbert space H and let X and Y be operators in B(H). Then the following are equivalent: (1) $$sup{frac{{parallel}E^{ot}Yf{parallel}}{{overline}{parallel}E^{ot}Xf{parallel}};:;f{epsilon}H,;E{epsilon}L}};<;{infty},;sup{frac{{parallel}Xf{parallel}}{{overline}{parallel}Yf{parallel}};:;f{epsilon}H};<;{infty}$$ and $ar{range;X}=H=ar{range;Y}$. (2) There exists an invertible operator A in AlgL such that AX=Y.