The inverse interpolation problem for operators

The inverse problem for a real interpolation functor in the class of ideal spaces is discussed. The most complete solution is obtained for consistent interpolation couples. It follows from the theorems proved in this article and from the concepts introduced that the Marcinkiewicz theorem on interpolation of weak type operators cannot essentially be strengthened.Translated fromMatematicheskie Zametki, Vol. 59, No. 3, pp. 323–333, May, 1996.