Similarity Problems and Completely Bounded Maps

• Main Author: Pisier, Gilles (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
• Edition: 2nd ed. 2001.
• Series: Lecture Notes in Mathematics, 1618
• Subjects: Functional analysis.; Harmonic analysis.; Functional Analysis.; Abstract Harmonic Analysis.

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 alg...

Table of Contents:

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