Fredholm Theory in Banach Spaces (Cambridge Tracts in Mathematics, Series Number 86)

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. In this tract Dr Ruston presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind. Every effort has been made to keep the presentation as elementary as possible, using arguments that do not require a very advanced background, for those working in the general area of functional analysis and its applications. For convenience, as in the theory of normed spaces, we shall use the word 'scalar' to mean either 'real number' or 'complex number' according to taste.