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＜電子ブック＞
An Introductory Course in Functional Analysis / by Adam Bowers, Nigel J. Kalton
(Universitext. ISSN:21916675)

版	1st ed. 2014.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	XVI, 232 p. 2 illus : online resource
著者標目	*Bowers, Adam author Kalton, Nigel J author SpringerLink (Online service)
件　名	LCSH:Functional analysis FREE:Functional Analysis
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4939-1945-1

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