Niveau: Supérieur, Doctorat, Bac+8
Introduction This set of notes was prepared for a mini-course given at the 27th Coloquio Brasileiro de Matematica. The purpose of the course is to introduce some key notions of the theory of C*-algebras and to illustrate them by examples originating from dynamical systems. It is very close in spirit to [31], written more than thirty years ago. Of course the subject has undergone many exciting developments since then, but at the elementary level of these notes, the basic ideas remain unchanged and I have liberally borrowed material from [31]. The theory of operator algebras was initiated in a series of papers by Murray and von Neumann ([25]) in the 1930's and 1940's. One mo- tivation was undoubtedly to provide a mathematical foundation for the young and budding quantum mechanics of these days. As it is well known, observables of a quantum mechanical system are represented in this theory by operators on a Hilbert space. They generate opera- tor algebras which encode the symmetries of the system. The inter- play with quantum theory, including quantum field theory and quan- tum statistical mechanics has been present ever since. The notion of KMS states, briefly studied in Chapter 3, is an example of this in- teraction. These notes will deal almost exclusively with C*-algebras. They are norm closed sub-?-algebras of the algebra of all bounded operators on a Hilbert space.
- commutative topology
- quantum mechanical system
- algebras
- hausdorff locally compact
- ergodic theory
- hilbert space
- pact hausdorff
- compact spaces
- algebras has
- most general commutative