These notes are an expanded version of a set written for a course given to final-year
undergraduates at the University of Oxford.
A thorough understanding of the Oxford third-year b4 analysis course (an introduction
to Banach and Hilbert spaces) or its equivalent is a prerequisite for this material. We
use [24] as a compendium of results from that series of lectures. (Numbers in square
brackets refer to items in the bibliography.)
The author acknowledges his debt to all those from whom he has learnt functional
analysis, especially Professor D. A. Edwards, Dr G. R. Allen and Dr J. M. Lindsay. The
students attending the course were very helpful, especially Mr A. Evseev, Mr L. Taitz
and Ms P. Iley.
This document was typeset using LATEX2ε with Peter Wilson’s memoir class and the
AMS-LATEX and XY-pic packages. The index was produced with the aid of the MakeIndex
program.
This edition contains a few additional exercises and the electronic version is equipped
with hyperlinks, thanks to the hyperref package of Sebastian Rahtz and Heiko Oberdiek.