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 obtained the following : Let X ＝ ($x_{isigma(i)}$ and Y ＝ ($y_{ij}$ be operators in B(H) such that $X_{isigma(i)} eq;0$ for all i. Then the following statements are equivalent. (1) There exists an operator A in Alg L such that AX = Y, every E in L reduces A and A is a self-adjoint operator. (2) sup ${frac{parallel{sum^n}_{i=1}E_iYf_iparallel}{parallel{sum^n}_{i=1}E_iXf_iparallel}n;epsilon;N,E_i;epsilon;L and f_i;epsilon;H}$ < $infty$ and $x_{i,sigma(i)}y_{i,sigma(i)}$ is real for all i = 1,2, ....