Abstract
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 the n-operators satisfies the equation AX<TEX>$\_$</TEX>i/ : Y<TEX>$\_$</TEX>i/, for i = 1, 2 …, n. In this article, we obtained the following : Let X = (x<TEX>$\_$</TEX>ij/) and Y = (y<TEX>$\_$</TEX>ij/) be operators acting on H such that <TEX>$\varkappa$</TEX><TEX>$\_$</TEX> i<TEX>$\sigma$</TEX> (i)/ 0 for all i. Then the following statements are equivalent. (1) There exists a unitary operator A in Alg(equation omitted) such that AX = Y and every E in (equation omitted) reduces A. (2) sup{(equation omitted)}<<TEX>$\infty$</TEX> and (equation omitted) = 1 for all i = 1, 2, ….
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