Fredholm Theory in Banach Spaces

Anthony Francis Ruston

doi:10.1017/CBO9780511569180

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.

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Fredholm Theory in Banach Spaces

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-x

1 - Introduction
pp 1-16

2 - Asymptotically quasi-compact operators and the Riesz theory
pp 17-41

3 - Tensor products of normed spaces
pp 42-77

4 - Fredholm theory for operators of finite rank
pp 78-117

5 - Operators with a Fredholm determinant
pp 118-134

6 - Fredholm formulae and the Riesz theory
pp 135-165

7 - Fredholm formulae for special classes of operators
pp 166-213

8 - Notes and Comments
pp 214-249

Bibliography
pp 250-284

Index of notations
pp 285-287

Subject index
pp 288-293

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