ON INESSENTIAL AND IMPROJECTIVE OPERATORS

We give several characterizations of the improjective operators, intro duced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would pro vide, for example, an intrinsic characterization of the inessential op erators. We give several equivalent formulations of this problem and w e show that the inessential operators acting between certain pairs of Banach spaces coincide with the improjective operators.