Ebook: Banach Space Theory: The Basis for Linear and Nonlinear Analysis

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.

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Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikod?m property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.

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Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikod?m property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Content:
Front Matter....Pages i-xiii
Basic Concepts in Banach Spaces....Pages 1-52
Hahn–Banach and Banach Open Mapping Theorems....Pages 53-81
Weak Topologies and Banach Spaces....Pages 83-177
Schauder Bases....Pages 179-235
Structure of Banach Spaces....Pages 237-289
Finite-Dimensional Spaces....Pages 291-330
Optimization....Pages 331-382
C 1-Smoothness in Separable Spaces....Pages 383-427
Superreflexive Spaces....Pages 429-463
Higher Order Smoothness....Pages 465-477
Dentability and Differentiability....Pages 479-519
Basics in Nonlinear Geometric Analysis....Pages 521-574
Weakly Compactly Generated Spaces....Pages 575-616
Topics in Weak Topologies on Banach Spaces....Pages 617-656
Compact Operators on Banach Spaces....Pages 657-685
Tensor Products....Pages 687-732
Appendix....Pages 733-749
Back Matter....Pages 751-820

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Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikod?m property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.
Content:
Front Matter....Pages i-xiii
Basic Concepts in Banach Spaces....Pages 1-52
Hahn–Banach and Banach Open Mapping Theorems....Pages 53-81
Weak Topologies and Banach Spaces....Pages 83-177
Schauder Bases....Pages 179-235
Structure of Banach Spaces....Pages 237-289
Finite-Dimensional Spaces....Pages 291-330
Optimization....Pages 331-382
C 1-Smoothness in Separable Spaces....Pages 383-427
Superreflexive Spaces....Pages 429-463
Higher Order Smoothness....Pages 465-477
Dentability and Differentiability....Pages 479-519
Basics in Nonlinear Geometric Analysis....Pages 521-574
Weakly Compactly Generated Spaces....Pages 575-616
Topics in Weak Topologies on Banach Spaces....Pages 617-656
Compact Operators on Banach Spaces....Pages 657-685
Tensor Products....Pages 687-732
Appendix....Pages 733-749
Back Matter....Pages 751-820
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