Given operators X and Y acting on a Hilbert space

, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation

, for

. In this article, we obtained the following : Let

be a Hilbert space and let

be a commutative subspace lattice on

. Let X and Y be operators acting on

. Then the following statements are equivalent. (1) There exists an operator A in

such that AX = Y, A is positive and every E in

reduces A. (2) sup

and $f_i{\in}{\mathcal{H}}<{\infty}$ and <

, ${\sum}^n_{i=1}\;E_iX\;f_i>\;{\geq}0$,

,

and

.