03244nam 22006015 450 991029998720332120200630151234.01-4939-1945-810.1007/978-1-4939-1945-1(CKB)3710000000324979(SSID)ssj0001408283(PQKBManifestationID)11856284(PQKBTitleCode)TC0001408283(PQKBWorkID)11347433(PQKB)10983923(DE-He213)978-1-4939-1945-1(MiAaPQ)EBC6313174(MiAaPQ)EBC5594856(Au-PeEL)EBL5594856(OCoLC)899068896(PPN)183153189(EXLCZ)99371000000032497920141211d2014 u| 0engurnn|008mamaatxtccrAn Introductory Course in Functional Analysis /by Adam Bowers, Nigel J. Kalton1st ed. 2014.New York, NY :Springer New York :Imprint: Springer,2014.1 online resource (XVI, 232 p. 2 illus.) Universitext,0172-5939Bibliographic Level Mode of Issuance: Monograph1-4939-1944-X Includes bibliographical references and index.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.Universitext,0172-5939Functional analysisFunctional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Functional analysis.Functional Analysis.515.7Bowers Adamauthttp://id.loc.gov/vocabulary/relators/aut722022Kalton Nigel Jauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299987203321An Introductory Course in Functional Analysis2508618UNINA