Background Information

Abstract

This chapter is of an auxiliary character. Its first section contains facts necessary for the further explanations concerning lineals of finite codimension as well as semi-Fredholm and Fredholm operators in Banach spaces. Most of these statements are well-known and have been published in several recent monographs.¹⁾ However, Theorem 1.12 on the Fredholmness of block operators and the local principle in the theory of Fredholm operators make an exception. The latter was proved in the form we need only in SIMONENKO’s paper [5]. Therefore, Theorems 1.12 and 1.14 will be given with detailed proofs. The remaining theorems in Section 1.1 we state without proof, referring the reader in every case to available sources. We do not intend to explain the history of semi-Fredholm and Fredholm operator theory, since this has already been excellently described (see, e.g. KATO [1]).