Pub. Date:
Springer Berlin Heidelberg
Similarity Problems and Completely Bounded Maps / Edition 2

Similarity Problems and Completely Bounded Maps / Edition 2

by Gilles Pisier


Current price is , Original price is $59.99. You
Select a Purchase Option (2nd exp. ed. 2001)
  • purchase options
  • purchase options


Similarity Problems and Completely Bounded Maps / Edition 2

These notes revolve around three similarity problems, appearing in three different contexts, but all dealing with the space B(H) of all bounded operators on a complex Hilbert space H. The first one deals with group representations, the second one with C* -algebras and the third one with the disc algebra. We describe them in detail in the introduction which follows. This volume is devoted to the background necessary to understand these three problems, to the solutions that are known in some special cases and to numerous related concepts, results, counterexamples or extensions which their investigation has generated. While the three problems seem different, it is possible to place them in a common framework using the key concept of "complete boundedness", which we present in detail. Using this notion, the three problems can all be formulated as asking whether "boundedness" implies "complete boundedness" for linear maps satisfying certain additional algebraic identities.

Product Details

ISBN-13: 9783540415244
Publisher: Springer Berlin Heidelberg
Publication date: 03/26/2001
Series: Lecture Notes in Mathematics , #1618
Edition description: 2nd exp. ed. 2001
Pages: 202
Product dimensions: 6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Introduction. Description of contents
1. Von Neumann's inequality and Ando's generalization
2. Non-unitarizable uniformly bounded group representations
3. Completely bounded maps
4. Completely bounded homomorphisms and derivations
5. Schur multipliers and Grothendieck's inequality
6. Hankelian Schur multipliers. Herz-Schur multipliers
7. The similarity problem for cyclic homomorphisms on a C*-algebra
8. Completely bounded maps in the Banach space setting
9. The Sz.-Nagy-Halmos similarity problem
10. The Kadison Similarity Problem
!Subject Index Notation Index

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews