http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Lifting solutions to perturbing problems in C*-algebras
The techniques of universal algebra are applied to the category of C*-algebras. An important difference, central to this book, is that one can consider approximate representations of relations and approximately commuting diagrams. Moreover, the highly algebraic approach does not exclude applications to very geometric C*-algebras. K-theory is avoided, but universal properties and stability properties of specific C*-algebras that have applications to K-theory are considered. Index theory arises naturally, and very concretely, as an obstruction to stability for almost commuting matrices. Multiplier algebras are studied in detail, both in the setting of rings and of C*-algebras. Recent results about extensions of C*-algebras are discussed, including a result linking amalgamated products with the Busby/Hochshild theory.
Ch. 0. Introduction -- Ch. 1. [sigma]-Unital C*-Algebras -- Ch. 2. Order and Factoring -- Ch. 3. Generators and Relations -- Ch. 4. Basic Perturbation -- Ch. 5. Push-Outs and Pull-Backs -- Ch. 6. Matrix algebras -- Ch. 7. Multipliers -- Ch. 8. Easy Lifting -- Ch. 9. Multiplier Algebras -- Ch. 10. Projectivity -- Ch. 11. Properties of Projective C*-Algebras -- Ch. 12. Heavy Lifting -- Ch. 13. Inductive Limits -- Ch. 14. Stable Relations -- Ch. 15. Applications -- Ch. 16. Extensions -- Ch. 17. Normals, Limits -- Ch. 18. Almost Normal Elements -- Ch. 19. Almost Normal Matrices.
Includes bibliographical references (pages 157-164) and index.
At head of title: The Fields Institute for Research in Mathematical Sciences.