What is this course all about?
An operator algebra on a Hilbert space H is a closed subalgebra of the algebra B(H) of bounded operators on H. These include all closed algebras of continuous functions on a compact space, matrix algebras, and many more. My intention is to divide the course into two halves: the first will focus on operator algebras, with the first few weeks dedicated to self-adjoint ones, namely C*-algebras, and the second will be devoted to the fruitful interaction between operator algebras and groups
The very flexible plan is:
- C*-algebras (3–5 lectures)
- Operator algebras and operator systems (3–4 lectures)
- Groups, dynamics, and related operator algebras (5–7 lectures)