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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