Summing and Nuclear Norms in Banach Space Theory

This textbook is an introduction to the techniques of summing and nuclear norms.

G. J. O. Jameson (Author)

9780521349376, Cambridge University Press

Paperback, published 30 July 1987

188 pages
22.9 x 15.4 x 1.1 cm, 0.3 kg

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.

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.

Subject Areas: Probability & statistics [PBT]