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Matrix Editions
Functional Analysis Volume I: A Gentle Introduction
by Dzung Minh Ha
$68
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640 pages, Hardcover
Table of Contents
Chapter 0: three important inequalities 1
Chapter 1: Metric and topological spaces 6
1.1 Metrics and metric spaces
1.2 Open and closed sets
1.3 Topological spaces
1.4 Continuous functions
1.5 Open sets and continuity
1.6 Some important topological concepts
1.7 Convergence of sequences in metric spaces
1.8 Completeness
1.9 Density, separability, and approximation
1.10 Metric space completions
1.11 Compactness
1.12 The Banach fixed point theorem
1.13 Baire's category theoremChapter 2: Normed spaces 116
2.1 Linear operators on function spaces
2.2 Hamel bases
2.3 Norms and normed spaces
2.4 Topological concepts in normed spaces
2.5 Topological vector spaces
2.6 Kolmogorov's theorem
2.7 Banach spaces
2.8 Infinite series in normed spaces
2.9 Schauder bases
2.10 Linear functionals and hyperplanes
2.11 Constructing new normed spacesChapter 3: Operators on normed spaces 206
3.1 Continuous linear maps
3.2 Integral operators
3.3 Linear homeomorphisms
3.4 Three important theorems
3.5 The normed space B(X,Y)
3.6 Complementary subspaces and projections
3.7 Riesz's lemma
3.8 The spectrum of a bounded linear operator
3.9 Continuous linear functionals and dual spacesChapter 4: Inner product spaces 291
4.1 Definitions and examples
4.2 Orthogonality
4.3 Unitary isomorphisms
4.4 Inner product spaces: three problems
4.5 Three characterizations for Hilbert spaces
4.6 Hilbert bases
Chapter 5: The Banach space C(X) 365
5.1 The Arzela-Ascoli theorem
5.2 Korovkin's theorem and the Weierstrass approximation theorem
5.3 Sub-algebras
5.4 The Stone-Weierstrass theoremChapter 6: Additional topics 415
6.1 The Baire-Osgood theorem
6.2 Gram determinants and Muntz's theorem
6.3 Differential equationsAppendix A: Set theory and functions 464
A.1 Sets
A.2 Relations
A.3 Zorn's lemma and the axiom of choice
A.4 Functions
A.5 Cardinality
A.6 The axiom of completeness on RAppendix B: Mostly linear algebra (a brief review) 480
B.1 Polynomials and sequences
B.2 Vector spaces
B.3 Linear independence and span
B.4 Bases and dimension
B.5 Linear transformations
B.6 Partial derivatives and the mean value theorem
B.7 Riemann integralsAppendix C: Some technical results 491
Appendix D: Solutions to odd-numbered exercises 494
Bibliography 618
Notation 622
Index 624
ISBN 978-0-9715766-1-2
640 pages, Hardcover, smythe-sewn binding
$65.Order information: books shipped within the United States
April 20, 2006