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Serious
mathematics, written with the reader in mind.

** **Matrix Editions

Functional AnalysisVolume I:A Gentle Introductionby Dzung Minh Ha

$68

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640 pages, Hardcover

Table of ContentsChapter 0: three important inequalities

1Chapter 1: Metric and topological spaces

61.1 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

1162.1 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

2063.1 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

2914.1 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)

3655.1 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

4156.1 The Baire-Osgood theorem

6.2 Gram determinants and Muntz's theorem

6.3 Differential equationsAppendix A: Set theory and functions

464A.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 onRAppendix B: Mostly linear algebra (a brief review)

480B.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

491Appendix D: Solutions to odd-numbered exercises

494Bibliography

618Notation

622Index

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