The main aim of this paper is to prove novel results on stability of the semi-Fredholm property of operators on interpolation spaces generated by interpolation functors. The methods are based on some general ideas we develop in the paper. This allows us to extend some previous work in literature to the abstract setting. We show an application to interpolation methods introduced by Cwikel–Kalton–Milman–Rochberg which includes, as special cases, the real and complex methods up to equivalence of norms and also some other well known methods of interpolation. A by-product of these results get the stability of isomorphisms on Calderón products of Banach function lattices. We also study the important characteristics in operator Banach space theory, the so-called modules of injection and surjection, and we prove interpolation estimates of these modules of operators on scales of the Calderón complex interpolation spaces.

本文的主要目的是证明关于算子的半-Fredholm性质在由内插函子生成的内插空间上的稳定性的新结果。这些方法基于我们在本文中提出的一些一般思想。这使我们可以将先前的一些文学著作扩展到抽象背景。我们展示了由Cwikel–Kalton–Milman–Rochberg引入的插值方法的一种应用，其中包括作为特殊情况的实数和复数，直到规范的等价性，以及一些其他众所周知的插值方法。这些结果的副产品在Banach函数格的Calderón乘积上获得了同构的稳定性。我们还研究了算子Banach空间理论中的重要特征，即所谓的注入和超越模块，