Introductory Course in Functional Analysis

Nigel Kalton (1946–2010) was Curators' Professor of Mathematics at the University of Missouri. Adam Bowers is a mathematics lecturer at the University of California, San Diego.

• 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.

"The text is very well written. Great care is taken to discuss interrelations of results. ... Each chapter ends with well selected exercises, typically around 20 exercises per chapter. ... I believe that this book is also suitable for self-study by an interested student. It can also serve as an excellent, concise reference for researchers in any area of mathematics seeking to recall/clarify fundamental concepts/results from functional analysis, in their proper context." (Beata Randrianantoanina, zbMATH 1328.46001, 2016) "The book is a nicely and economically designed introduction to functional analysis, with emphasis on Banach spaces, that is well-suited for a one- or two-semester course." (M. Kunzinger, Monatshefte fur Mathematik, Vol. 181, 2016)