Research Group:

## Mathematical Methods in Quantum Statistical Physics

venue and schedule: Mo + Tue, 9:15-11:00, room A-136; Tue 31 Jan in A-132

start: 16 January 2017

duration**:** 40 hours (2 cycles); partial credits are possible**office hours:** Tue, 15:00-16:00, office A-724

## Introduction to C*-algebras and applications

This course provides a brief introduction to C*-algebras. The course will cover at least the following topics:

- brief recap on Banach spaces and linear operators;

- Banach algebras: spectrum, Gelfand transform, Stone-Weierstrass theorem;

- C*-algebras: definition and basic properties;

- Gelfand-Naimark duality between commutative C*-algebras and locally compact Hausdorff spaces;

- continuous functional calculus;

- GNS (Gelfand-Naimark-Segal) construction.