On inessential and improjective operators.
Tom 131 / 1998
Studia Mathematica 131 (1998), 271-287 DOI: 10.4064/sm-131-3-271-287
We give several characterizations of the improjective operators, introduced 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 provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of Banach spaces coincide with the improjective operators.