In this tract, Dr Ruston presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind. Much of the presentation is based on research carried out over the last twenty-five years and has never appeared in book form before. Dr Ruston begins with the construction for operators of finite rank, using Fredholm's original method as a guide. He then considers formulae that have structure similar to those obtained by Fredholm, using, and developing further, the relationship with Riesz theory. In particular, he obtains bases for the finite-dimensional subspaces figuring in the Riesz theory. Finally he returns to the study of specific constructions for various classes of operators. Dr Ruston has made every effort to keep the presentation as elementary as possible, using arguments that do not require a very advanced background. Thus the book can be read with profit by graduate students as well as specialists working in the general area of functional analysis and its applications.
Table of ContentsPreface; 1. Introduction; 2. Asymptotically quasi-compact operators and the Riesz theory; 3. Tensor products of normed spaces; 4. Fredholm theory for operators of finite rank; 5. Operators with a Fredholm determinant; 6. Fredholm formulae and the Riesz theory; 7. Fredholm formulae for special classes of operators; 8. Notes and comments; Bibliography; Index of notations; Subject index.