Beschreibung:
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 Hahn-Banach theorem based on an inf-convolution technique, the proof of Schauder's theorem, and the proof of the Milman-Pettis theorem.
Foreword.- Preface.- 1 Introduction.- 2 Classical Banach spaces and their duals.- 3 The Hahn-Banach 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.