Overview

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.

Full Product Details

Author:   J. R. Giles (University of Newcastle, New South Wales)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
Volume:   13
ISBN:  

9781139168465

ISBN 10:   1139168460
Publication Date:   05 June 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   Available To Order  
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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.

Reviews

'... the text is up-to-date and detailed in exposition, and is large enough in material covered for different courses to be constructed from it ...'. Australian Mathematical Society Gazette

'... the text is up-to-date and detailed in exposition, and is large enough in material covered for different courses to be constructed from it ...'. Australian Mathematical Society Gazette 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

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