This textbook is an introduction to the techniques of summing and nuclear norms. The author's aim is to present a clear and simple account of these ideas and to demonstrate the power of their application to a variety of Banach space questions. The style is expository and the only prerequisite is a beginner's course on Wormed linear spaces and a minimal knowledge of functional analysis. Thus, Dr Jameson is able to concentrate on important, central results and gives concrete and largely non-technical proofs, often supplying alternative proofs which both contribute something to the understanding. Final-year undergraduates and postgraduates in functional analysis will enjoy this introduction to the subject, and there are many examples and exercises throughout the text to help the reader and to demonstrate the range of application these techniques find. A list of references indicates the way for further reading.
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: July 1987
- format: Paperback
- isbn: 9780521349376
- length: 188 pages
- dimensions: 229 x 154 x 11 mm
- weight: 0.3kg
- availability: Available
Table of Contents
0. Banach space background
1. Finite rank operators: trace and 1-nuclear norm
2. Finite sequences of elements : the quantities µ1, µ2
3. The summing norms
4. Other nuclear norms: duality with the summing norms
5. Pietsch's theorem and its applications
6. Averaging: type 2 and cotype 2 constants
7. More averaging: Khinchin's inequality and related results
8. Integral methods: Gaussian averaging
9. 2-dominated spaces
10. Grothendieck's inequality
11. The interpolation method for Grothendieck-type theorems
12. Results connected with the basis constant
13. Estimation of summing norms using a restricted number of elements
14. Pisier's theorem for pi2,1
15. Tensor products of operators
16. Trace duality revisited: integral norms
17. Applications of local reflexivity
18. Cone-summing norms.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email firstname.lastname@example.orgRegister Sign in
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 ×
Are you sure you want to delete your account?
This cannot be undone.
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.×