Banach bundles and linear operators

This paper has the character of a survey. In it we consider questions in the theory of Fredholm (Noether) and semi-Fredholm operators on a Banach space that depend on a many-dimensional parameter. The paper divides naturally into two parts: the theory of operators depending continuously on a parameter (§ 1–2), and the theory of operators depending holomorphically on a parameter (§ 3–5). The theory of Banach bundles provides a natural apparatus for the study of these questions. In this connection we give a detailed account of a number of parts of this theory.
In addition, we quote, with proofs, some fundamental facts in functional analysis that have been obtained in the past ten or twenty years and are not well represented in the monographs and text-books.