LEADER 04587nam 22006375 450 001 9910960442503321 005 20250731082142.0 010 $a1-4612-0603-0 024 7 $a10.1007/978-1-4612-0603-3 035 $a(CKB)3400000000089196 035 $a(SSID)ssj0001297183 035 $a(PQKBManifestationID)11721715 035 $a(PQKBTitleCode)TC0001297183 035 $a(PQKBWorkID)11354707 035 $a(PQKB)10497994 035 $a(DE-He213)978-1-4612-0603-3 035 $a(MiAaPQ)EBC3075035 035 $a(PPN)238007022 035 $a(EXLCZ)993400000000089196 100 $a20121227d1998 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 13$aAn Introduction to Banach Space Theory /$fby Robert E. Megginson 205 $a1st ed. 1998. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1998. 215 $a1 online resource (XIX, 599 p.) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v183 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a0-387-98431-3 311 08$a1-4612-6835-4 320 $aIncludes bibliographical references and index. 327 $a1 Basic Concepts -- 1.1 Preliminaries -- 1.2 Norms -- 1.3 First Properties of Normed Spaces -- 1.4 Linear Operators Between Normed Spaces -- 1.5 Baire Category -- 1.6 Three Fundamental Theorems -- 1.7 Quotient Spaces -- 1.8 Direct Sums -- 1.9 The Hahn-Banach Extension Theorems -- 1.10 Dual Spaces -- 1.11 The Second Dual and Reflexivity -- 1.12 Separability -- 1.13 Characterizations of Reflexivity -- 2 The Weak and Weak Topologies -- 2.1 Topology and Nets -- 2.2 Vector Topologies -- 2.3 Metrizable Vector Topologies -- 2.4 Topologies Induced by Families of Functions -- 2.5 The Weak Topology -- 2.6 The Weak Topology -- 2.7 The Bounded Weak Topology -- 2.8 Weak Compactness -- 2.9 James?s Weak Compactness Theorem -- 2.10 Extreme Points -- 2.11 Support Points and Subreflexivity -- 3 Linear Operators -- 3.1 Adjoint Operators -- 3.2 Projections and Complemented Subspaces -- 3.3 Banach Algebras and Spectra -- 3.4 Compact Operators -- 3.5 Weakly Compact Operators -- 4 Schauder Bases -- 4.1 First Properties of Schauder Bases -- 4.2 Unconditional Bases -- 4.3 Equivalent Bases -- 4.4 Bases and Duality -- 4.5 James?s Space J -- 5 Rotundity and Smoothness -- 5.1 Rotundity -- 5.2 Uniform Rotundity -- 5.3 Generalizations of Uniform Rotundity -- 5.4 Smoothness -- 5.5 Uniform Smoothness -- 5.6 Generalizations of Uniform Smoothness -- A Prerequisites -- B Metric Spaces -- D Ultranets -- References -- List of Symbols. 330 $aMany important reference works in Banach space theory have appeared since Banach's "Théorie des Opérations Linéaires", the impetus for the development of much of the modern theory in this field. While these works are classical starting points for the graduate student wishing to do research in Banach space theory, they can be formidable reading for the student who has just completed a course in measure theory and integration that introduces the L_p spaces and would like to know more about Banach spaces in general. The purpose of this book is to bridge this gap and provide an introduction to the basic theory of Banach spaces and functional analysis. It prepares students for further study of both the classical works and current research. It is accessible to students who understand the basic properties of L_p spaces but have not had a course in functional analysis. The book is sprinkled liberally with examples, historical notes, and references to original sources. Over 450 exercises provide supplementary examples and counterexamples and give students practice in the use of the results developed in the text. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v183 606 $aMathematical analysis 606 $aMathematical physics 606 $aAnalysis 606 $aMathematical Methods in Physics 606 $aTheoretical, Mathematical and Computational Physics 615 0$aMathematical analysis. 615 0$aMathematical physics. 615 14$aAnalysis. 615 24$aMathematical Methods in Physics. 615 24$aTheoretical, Mathematical and Computational Physics. 676 $a515 700 $aMegginson$b Robert E.$4aut$4http://id.loc.gov/vocabulary/relators/aut$062515 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910960442503321 996 $aIntroduction to Banach space theory$979336 997 $aUNINA