Activity: Visiting an external institution types › Research and Teaching at External Organisation
Derivations on Banach and C*-algebras
8-hour graduate course. In this course I will aim to highlight some of the interesting properties of the important class of derivations on Banach and C*-algebras. For instance, derivations serve as the infinitesimal generators of reversible dynamics and thus are fundamental in some areas of Physics. The course will not assume any familiarity with Banach algebras, though. We shall start with the basic definitions, discuss spectral theory in Banach and C*-algebras, and develop the Gelfand theory of commutative semisimple Banach algebras. We shall study the functional calculus, with an emphasis on the functional calculus in C*-algebras. Armed with these tools, we shall investigate some of the properties of derivations. Prerequisites are a course in basic functional analysis and some familiarity with topological spaces though the course will be tailored to the needs and knowledge of the participants.