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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.

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.

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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.

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"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 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 für Mathematik, Vol. 181, 2016)

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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.

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