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Introduction to the Analysis of Normed Linear Spaces

Introduction to the Analysis of Normed Linear Spaces

£50.99

textbook

Part of Australian Mathematical Society Lecture Series

  • Author: J. R. Giles, University of Newcastle, New South Wales
  • Date Published: April 2000
  • availability: Available
  • format: Paperback
  • isbn: 9780521653756

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About the Authors
  • 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.

    • 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
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    Reviews & endorsements

    '… 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

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    Product details

    • Date Published: April 2000
    • format: Paperback
    • isbn: 9780521653756
    • length: 296 pages
    • dimensions: 229 x 152 x 17 mm
    • weight: 0.44kg
    • contains: 19 b/w illus. 203 exercises
    • availability: 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.

  • Author

    J. R. Giles, University of Newcastle, New South Wales

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