Linear Analysis: An Introductory Course

by Béla Bollobás

Now revised and updated, this brisk introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have had some background in real analysis. The author's aim is not just to cover the standard material in a standard way, but to present results of application in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include the geometry of finite-dimensional spaces, invariant subspaces, fixed-point theorems, and the Bishop-Phelps theorem. An outstanding feature is the large number of exercises, some straightforward, some challenging, none uninteresting.

Genres: Mathematics

256 pages, Paperback

First published November 30, 1990

Reviews

[Nicholas Wilson · Rating 5 out of 5]

It’s been a long journey, but after dipping into the book for years, I think I’ve finally had the stamina to learn all the proofs and finish it off. It’s very rewarding to take a break from focussing on lectures and get and understanding and overview of the subject instead. Bollobás is very clear, thorough, and I don’t think there are any mistakes (beyond the usual deliberate details lost in conciseness). The exercises also are good. One of the half dozen best books to read to get the full flavour of undergrad maths.