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Graduate Texts in Mathematics Ser.: Introduction to Banach Space Theory by Robert E. Megginson (1998, Hardcover)
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About this product
Product Identifiers
PublisherSpringer New York
ISBN-100387984313
ISBN-139780387984315
eBay Product ID (ePID)533174
Product Key Features
Number of PagesXix, 599 Pages
LanguageEnglish
Publication NameIntroduction to Banach Space Theory
Publication Year1998
SubjectFunctional Analysis, Physics / Mathematical & Computational, Mathematical Analysis
TypeTextbook
AuthorRobert E. Megginson
Subject AreaMathematics, Science
SeriesGraduate Texts in Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.5 in
Item Weight81.5 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN97-052159
Dewey Edition21
TitleLeadingAn
Series Volume Number183
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal515/.732
Table Of Content1 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.
SynopsisPreparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples., This book is an introduction to the general theory of Banach spaces, designed to prepare the reader with a background in functional analysis that will enable him or her to tackle more advanced literature in the subject. The book is replete with examples, historical notes, and citations, as well as nearly 500 exercises., Many 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., The purpose of this book is to bridge this gap and provide an introduction to the general theory of Banach spaces and functional analysis. It prepares students for further study of both the classical works and current resarch. It is accessible to students who have had a course in real and complex analysis and understand the basic properties of L_p spaces. The book is sprinkled liberally with examples, historical notes, citations, and original sources. Over 450 exercises provide students with practice in the use of the results developed in the text through supplementary examples and couterexamples.
LC Classification NumberQA299.6-433
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