Introduction to the Analysis of Normed Linear Spaces
Introduction to the Analysis of Normed Linear Spaces
$99.99
USDThis text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. Giles illustrates the general theory with a great variety of example spaces.
- Can be treated as a sequel to Giles' previous book
- Author has many years teaching experience in this area
- Text requires very little background knowledge of the reader
Reviews & endorsements
"The book is very well written and the level is appropriate for the intended audience...It is easy to read and covers many interesting topics...a useful resource for basic and standard normed linear space theory...an excellent text." Mathematical Reviews
Product details
March 2000Paperback
9780521653756
296 pages
229 × 152 × 17 mm
0.44kg
19 b/w illus. 203 exercises
Available
Table of Contents
- 1. Basic properties of normed linear spaces
- 2. Classes of example spaces
- 3. Orthonormal sets in inner product spaces
- 4. Norming mappings and forming duals and operator algebras
- 5. The shape of the dual
- 6. The Hahn–Banach theorem
- 7. The natural embedding and reflexivity
- 8. Subreflexivity
- 9. Baire category theory for metric spaces
- 10. The open mapping and closed graph theorems
- 11. The uniform boundedness theorem
- 12. Conjugate mappings
- 13. Adjoint operators on Hilbert space
- 14. Projection operators
- 15. Compact operators
- 16. The spectrum
- 17. The spectrum of a continuous linear operator
- 18. The spectrum of a compact operator
- 19. The spectral theorem for compact normal operators on Hilbert space
- 20. The spectral theorem for compact operators on Hilbert space
- Appendices. A1. Zorn's lemma
- A2. Numerical equivalence
- A3. Hamel basis.
