Hilbert C*-Modules
A Toolkit for Operator Algebraists

This book provides, for the first time, a clear and unified exposition of the main techniques and results in operator algebras.

E. Christopher Lance (Author)

9780521479103, Cambridge University Press

Paperback, published 16 March 1995

144 pages
22.6 x 15.1 x 0.8 cm, 0.208 kg

"This is a delightful volume and a worthy addition to the literature on C*-algebras." Robert S. Doran, Mathematical Reviews

Hilbert C*-modules are objects like Hilbert spaces, except that the inner product, instead of being complex valued, takes its values in a C*-algebra. The theory of these modules, together with their bounded and unbounded operators, is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebras. This book is based on a series of lectures given by Professor Lance at a summer school at the University of Trondheim. It provides, for the first time, a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. It will be welcomed as an excellent resource for all graduate students and researchers working in operator algebras.

1. Modules
2. Multipliers and morphisms
3. Projections and unitaries
4. Tensor products
5. The KSGNS construction
6. Stabilisation or absorption
7. Full modules, Morita equivalence
8. Slice maps and bialgebras
9. Unbounded operators
10. The bounded transform, unbounded multipliers.

Subject Areas: Functional analysis & transforms [PBKF]