Lectures On Some Fixed Point Theorems Of Functional Analysis

No part of this book may be reproduced in any form by print, microfilm or any other means without written permission from the Introduction These lectures do not constitute a systematic account of fixed point theorems. I have said nothing about these theorems where the interest is essentially topological, and in particular have nowhere introduced the important concept of mapping degree. The lectures have been concerned with the application of a variety of methods to both non-linear (fixed point) problems and linear (eigenvalue) problems in infinite dimensional spaces. A wide choice of techniques is available for linear problems, and I have usually chosen to use those that give something more than existence theorems, or at least a promise of something more. That is, I have been interested not merely in existence theorems, but also in the construction of eigenvectors and eigenvalues. For this reason, I have chosen elementary rather than elegant methods. I would like to draw special attention to the Appendix in which I give the solution due to B. V. Singbal of a problem that I raised in the course of the lectures. I am grateful to Miss K. B. Vedak for preparing these notes and seeing to their publication.