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First Course in Functional Analysis

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ISBN-10: 0470146192

ISBN-13: 9780470146194

Edition: 2008

Authors: S. David Promislow

List price: $169.95
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This straight-forward, concise book is made up of carefully selected topics and is written in an accessible that requires minimal background knowledge. It provides the reader with a sense of unity in the subject's development and fully explains the essential concepts, outlining the logic behind the steps to familiarize the reader with the theories. All the important topics are covered, from linear spaces and topological vector spaces, to the main theorems such as the Major Banach Space Theorems and the Hahn-Banach Theorem. Numerous exercises of ranging difficulty are included throughout the text to enhance the reader's learning.
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Book details

List price: $169.95
Copyright year: 2008
Publisher: John Wiley & Sons, Incorporated
Publication date: 4/25/2008
Binding: Hardcover
Pages: 328
Size: 6.50" wide x 9.60" long x 0.88" tall
Weight: 1.496
Language: English

Linear Spaces and Operators
Linear Spaces
Linear Operators
Passage from Finite- to Infinite-Dimensional Spaces
Normed Linear Spaces: The Basics
Metric Spaces
Space of Bounded Functions
Bounded Linear Operators
Comparison of Norms
Quotient Spaces
Finite-Dimensional Normed Linear Spaces
L[superscript p] Spaces
Direct Products and Sums
Schauder Bases
Fixed Points and Contraction Mappings
Major Banach Space Theorems
Baire Category Theorem
Open Mappings
Bounded Inverses
Closed Linear Operators
Uniform Boundedness Principle
Hilbert Spaces
Semi-Inner Products
Nearest Points and Convexity
Linear Functionals on Hilbert Spaces
Linear Operators on Hilbert Spaces
Order Relation on Self-Adjoint Operators
Hahn-Banach Theorem
Basic Version of Hahn-Banach Theorem
Complex Version of Hahn-Banach Theorem
Application to Normed Linear Spaces
Geometric Versions of Hahn-Banach Theorem
Examples of Dual Spaces
Double Duals and Reflexivity
Weak and Weak* Convergence
Topological Linear Spaces
Review of General Topology
Topologies on Linear Spaces
Linear Functionals on Topological Linear Spaces
Weak Topology
Weak* Topology
Extreme Points and Krein-Milman Theorem
Operator Topologies
The Spectrum
Banach Algebras
General Properties of the Spectrum
Numerical Range
Spectrum of a Normal Operator
Functions of Operators
Brief Introduction to C*-Algebras
Compact Operators
Introduction and Basic Definitions
Compactness Criteria in Metric Spaces
New Compact Operators from Old
Spectrum of a Compact Operator
Compact Self-Adjoint Operators on Hilbert Spaces
Invariant Subspaces
Application to Integral and Differential Equations
Integral Operators
Integral Equations
Second-Order Linear Differential Equations
Sturm-Liouville Problems
First-Order Differential Equations
Spectral Theorem for Bounded, Self-Adjoint Operators
Introduction and Motivation
Spectral Decomposition
Extension of Functional Calculus
Multiplication Operators
Zorn's Lemma
Stone-Weierstrass Theorem
Basic Theorem
Nonunital Algebras
Complex Algebras
Extended Real Numbers and Limit Points of Sequences
Extended Reals
Limit Points of Sequences
Measure and Integration
Introduction and Notation
Basic Properties of Measures
Properties of Measurable Functions
Integral of a Nonnegative Function
Integral of an Extended Real-Valued Function
Integral of a Complex-Valued Function
Construction of Lebesgue Measure on R
Completeness of Measures
Signed and Complex Measures
Radon-Nikodym Derivatives
Product Measures
Riesz Representation Theorem
Tychonoff's Theorem