An Introductory Course in Functional Analysis

Based on a graduate course by the celebrated analyst Nigel Kalton, this well-balanced introduction to functional analysis makes clear not only how, but why, the field developed. All major topics belonging to a first course in functional analysis are covered. However, unlike traditional introductions to the subject, Banach spaces are emphasized over Hilbert spaces, and many details are presented in a novel manner, such as the proof of the HahnBanach theorem based on an inf-convolution technique, the proof of Schauder's theorem, and the proof of the MilmanPettis theorem.

With the inclusion of many illustrative examples and exercises, An Introductory Course in Functional Analysis equips the reader to apply the theory and to master its subtleties. It is therefore well-suited as a textbook for a one- or two-semester introductory course in functional analysis or as a companion for independent study.

Presents the basics of functional analysis according to Nigel Kalton, a leader in the field Enables the reader to appreciate and apply the theory by explaining both the why and how of the subject's development Gives novel proofs of major theorems, such as the HahnBanach theorem, Schauder's theorem, and the MilmanPettis theorem Contains over 150 exercises to develop and enrich the reader's understanding of the subject Includes supplementary material: sn.pub/extras

Autorentext
Nigel Kalton (19462010) was Curators' Professor of Mathematics at the University of Missouri. Adam Bowers is a mathematics lecturer at the University of California, San Diego.

Inhalt
Foreword.- Preface.- 1 Introduction.- 2 Classical Banach spaces and their duals.- 3 The HahnBanach theorems.- 4 Consequences of completeness.- 5 Consequences of convexity.- 6 Compact operators and Fredholm theory.- 7 Hilbert space theory.- 8 Banach algebras.- A Basics of measure theory.- B Results from other areas of mathematics.- References.- Index.