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Introduction to the Analysis of Normed Linear Spaces

Introduction to the Analysis of Normed Linear Spaces

$89.99 (X)

textbook

Part of Australian Mathematical Society Lecture Series

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

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About the Authors
  • This text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. Giles illustrates the general theory 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 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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    Product details

    • Date Published: March 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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