Linear Analysis

Revised and updated introduction to functional analysis.

Now revised and updated, this introduction to functional analysis is intended for advanced undergraduate students with some background in real analysis. The author includes results of application in contemporary mathematics and shows the relevance of functional analysis to other areas. An outstanding feature is the large number of exercises.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.