Skip to content
Register Sign in Wishlist

An Introduction to Functional Analysis

$46.99 (X)

textbook
  • Date Published: April 2020
  • availability: Available
  • format: Paperback
  • isbn: 9780521728393

$ 46.99 (X)
Paperback

Add to cart Add to wishlist

Other available formats:
Hardback, eBook


Request examination copy

Instructors may request a copy of this title for examination

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • This accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and the theory of partial differential equations. The treatment of Hilbert spaces covers the topics required to prove the Hilbert–Schmidt theorem, including orthonormal bases, the Riesz representation theorem, and the basics of spectral theory. The material on Banach spaces and their duals includes the Hahn–Banach theorem, the Krein–Milman theorem, and results based on the Baire category theorem, before culminating in a proof of sequential weak compactness in reflexive spaces. Arguments are presented in detail, and more than 200 fully-worked exercises are included to provide practice applying techniques and ideas beyond the major theorems. Familiarity with the basic theory of vector spaces and point-set topology is assumed, but knowledge of measure theory is not required, making this book ideal for upper undergraduate-level and beginning graduate-level courses.

    • Includes an extensive source of homework problems for instructors and independent study
    • Presents functional analytical methods without a reliance on measure-theoretic results, making the topics more widely accessible
    • Provides readers with a sense of accomplishment and closure by showing how both Hilbert space theory and Banach space theory aim towards major results with important applications
    Read more

    Reviews & endorsements

    ‘This excellent introduction to functional analysis brings the reader at a gentle pace from a rudimentary acquaintance with analysis to a command of the subject sufficient, for example, to start a rigorous study of partial differential equations. The choice and order of topics are very well thought-out, and there is a fine balance between general results and concrete examples and applications.' Charles Fefferman, Princeton University, New Jersey

    ‘An Introduction to Functional Analysis covers everything that one would expect to meet in an undergraduate course on this elegant area and more, including spectral theory, the category-based theorems and unbounded operators. With a well-written narrative and clear detailed proofs, together with plentiful examples and exercises, this is both an excellent course book and a valuable reference for those encountering functional analysis from across mathematics and science.' Kenneth Falconer, University of St Andrews, Scotland

    ‘This is a beautifully written book, containing a wealth of worked examples and exercises, covering the core of the theory of Banach and Hilbert spaces. The book will be of particular interest to those wishing to learn the basic functional analytic tools for the mathematical analysis of partial differential equations and the calculus of variations.' Endre Suli, University of Oxford

    '… this is a valuable book. It is an accessible yet serious look at the subject, and anybody who has worked through it will be rewarded with a good understanding of functional analysis, and should be in a position to read more advanced books with profit.' Mark Hunacek, The Mathematical Gazette

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: April 2020
    • format: Paperback
    • isbn: 9780521728393
    • length: 416 pages
    • dimensions: 227 x 153 x 22 mm
    • weight: 0.6kg
    • contains: 17 b/w illus. 215 exercises
    • availability: Available
  • Table of Contents

    Part I. Preliminaries:
    1. Vector spaces and bases
    2. Metric spaces
    Part II. Normed Linear Spaces:
    3. Norms and normed spaces
    4. Complete normed spaces
    5. Finite-dimensional normed spaces
    6. Spaces of continuous functions
    7. Completions and the Lebesgue spaces Lp(Ω)
    Part III. Hilbert Spaces:
    8. Hilbert spaces
    9. Orthonormal sets and orthonormal bases for Hilbert spaces
    10. Closest points and approximation
    11. Linear maps between normed spaces
    12. Dual spaces and the Riesz representation theorem
    13. The Hilbert adjoint of a linear operator
    14. The spectrum of a bounded linear operator
    15. Compact linear operators
    16. The Hilbert–Schmidt theorem
    17. Application: Sturm–Liouville problems
    Part IV. Banach Spaces:
    18. Dual spaces of Banach spaces
    19. The Hahn–Banach theorem
    20. Some applications of the Hahn–Banach theorem
    21. Convex subsets of Banach spaces
    22. The principle of uniform boundedness
    23. The open mapping, inverse mapping, and closed graph theorems
    24. Spectral theory for compact operators
    25. Unbounded operators on Hilbert spaces
    26. Reflexive spaces
    27. Weak and weak-* convergence
    Appendix A. Zorn's lemma
    Appendix B. Lebesgue integration
    Appendix C. The Banach–Alaoglu theorem
    Solutions to exercises
    References
    Index.

  • Author

    James C. Robinson, University of Warwick
    James C. Robinson is a professor in the Mathematics Institute at the University of Warwick. He has been the recipient of a Royal Society University Research Fellowship and an Engineering and Physical Sciences Research Council (EPSRC) Leadership Fellowship. He has written six books in addition to his many publications in infinite-dimensional dynamical systems, dimension theory, and partial differential equations.

Related Books

also by this author

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon
×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×