An introduction to the analysis of normed linear spaces

Abstract

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.