Elements of Functional Analysis

This 1970 textbook aims to provide a truly introductory course in functional analysis.

I. J. Maddox (Author)

9780521358682, Cambridge University Press

Paperback, published 26 January 1989

256 pages
22.8 x 15.1 x 1.5 cm, 0.35 kg

The second edition of this successful textbook, first published in 1970, retains the aims of the first, namely to provide a truly introductory course in functional analysis, but the opportunity has been taken to add more detail and worked examples. The main changes are complete revisons of the work on convex sets, metric and topological linear spaces, reflexivity and weak convergence. Additional material on the Weiner algebra of absolutely convergent Fourier series and on weak topologies is included. A final chapter includes elementary applications of functional analysis to differential and integral equations.

Preface to the second edition
Preface to the first edition
Part I. Basic Set Theory and Analysis: 1. Sets and functions
2. Real and complex numbers
3. Sequences of functions, continuity, differentiability
4. Inequalities
Part II. Metric and Topological Spaces: 1. Metric and semimetric spaces
2. Complete metric spaces
3. Some metric and topological concepts
4. Continuous functions on metric and topological spaces
5. Compact sets
6. Category and uniform boundedness
Part III. Linear and Linear Metric Spaces: 1. Linear spaces
2. Subspaces, dimensionality, factorspaces, convex sets
3. Metric linear spaces, topological linear spaces
4. Basis
Part IV. Normed Linear Spaces: 1. Convergence and completeness
2. Linear operators and functionals
3. The Banach–Steinhaus theorem
4. The open mapping and closed graph theorems
5. The Hahn–Banach extension
6. Weak topology and weak convergence
Part V. 1. Algebras and Banach algebras
2. Homomorphisms and isomorphisms
3. The spectrum and the Gelfand–Mazaur theorem
4. The Weiner algebra
Part VI. Hilbert Space: 1. Inner product and Hilbert spaces
2. Orthonormal sets
3. The dual space of a Hilbert space
4. Symmetric and compact operators
Part VII. Applications: 1. Differential and integral problems
2. The Sturm–Liouville problem
3. Matrix transformations in sequence spaces
Appendix
Bibliography
Index.

Subject Areas: Probability & statistics [PBT]