Hilbert C*-Modules A Toolkit for Operator Algebraists [Paperback]

This book provides, for the first time, a clear and unified exposition of the main techniques and results in operator algebras.Hilbert C*-modules are objects like Hilbert spaces except that the inner product, instead of being complex valued, takes its values in C*-algebra. This text provides a clear description of the main techniques and results in this area, including a substantial amount of new and unpublished material.Hilbert C*-modules are objects like Hilbert spaces except that the inner product, instead of being complex valued, takes its values in C*-algebra. This text provides a clear description of the main techniques and results in this area, including a substantial amount of new and unpublished material.The theory of these modules together with their bounded and unbounded operators is not only rich and attractive in its own right but forms an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 algebra. This book provides a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. Graduate students and researchers working in operator algebras will welcome this book as an excellent resource.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. This is a delightful volume and a worthy addition to the literature on C*-algebras. Robert S. Doran, Mathematical Reviews