INTRODUCTION TO THE ANALYSIS OF NORMED LINEAR SPACES

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This is a basic course in functional analysis for senior undergraduate and beginning postgraduate students.This is a basic course for senior undergraduate and beginning postgraduate students on the structural properties of normed linear spaces in general especially associated with dual spaces and continuous linear operators on normed linear spaces. The implications of the general theory are illustrated with a great variety of example spaces.This is a basic course for senior undergraduate and beginning postgraduate students on the structural properties of normed linear spaces in general especially associated with dual spaces and continuous linear operators on normed linear spaces. The implications of the general theory are illustrated with a great variety of example spaces.This text is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. It aims at providing some insight into basic abstract analysis which is now the contextual language of much modern mathematics. Although it is assumed that the student will have familiarity with elementary real and complex analysis and linear algebra and have studied a course in the analysis of metric spaces a knowledge of integration theory or general topology is not required. The theme of this text concerns structural properties of normed linear spaces in general especially associated with dual spaces and continuous linear operators on normed linear spaces. But the implications of the general theory are illustrated with a great variety of example spaces.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 HahnBanach 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. Zorns lemma: A2. Numerical equivalence: A3. Hamel basis. the text is uptodate and detailed in exposition and is large enough in material covered for different courses to be constructed from it . Australian Mathematical Society Gazette

Data Publikacji: 2000-03-13
Wymiary: 228 mm 152 mm 17 mm 440 gr