Synopses & Reviews
This is a basic course in functional analysis for senior undergraduate and beginning postgraduate students.
Review
"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
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.