Perturbation theory of p-adic Fredholm and semi-Fredholm operators

The main goal of this paper is to prove that Fredholm and semi-Fredholm operators between p-adic (or non-archimedean) Banach spaces, as well as the index of those that are Fredholm, are preserved when they are perturbed by a small operator. In this way we obtain the non-archimedean counterparts of some well-known results of classical Operator Theory. For non-spherically complete fields the classical techniques are no longer valid in the p-adic context, which forces us to seek a completely different way to attack the problem. The p-adic concept of orthogonality will be one of the key tools to get our purpose.