Skip to main content Accessibility help
Internet Explorer 11 is being discontinued by Microsoft in August 2021. If you have difficulties viewing the site on Internet Explorer 11 we recommend using a different browser such as Microsoft Edge, Google Chrome, Apple Safari or Mozilla Firefox.

Chapter 12: Dual Spaces and the Riesz Representation Theorem

Chapter 12: Dual Spaces and the Riesz Representation Theorem

pp. 153-158

Authors

, University of Warwick
Resources available Unlock the full potential of this textbook with additional resources. There are Instructor restricted resources available for this textbook. Explore resources
  • Add bookmark
  • Cite
  • Share

Summary

We introduce the dual space of a Banach space X, which is the collection of all bounded linear maps from X into the field K (‘linear functionals’), equipped with the corresponding operator norm. We prove the Riesz Representation Theorem, which shows that in a Hilbert space, any linear functional can be written as the inner product with some element of the Hilbert space.

Keywords

  • dual spaces
  • Riesz Representation Theorem

About the book

Access options

Review the options below to login to check your access.

Purchase options

eTextbook
US$50.00
Hardback
US$110.00
Paperback
US$50.00

Have an access code?

To redeem an access code, please log in with your personal login.

If you believe you should have access to this content, please contact your institutional librarian or consult our FAQ page for further information about accessing our content.

Also available to purchase from these educational ebook suppliers