Shuaibing Luo: Reducing subspaces of some function spaces

Abstract:

Suppose T is a bounded linear operator on a Hilbert space H. If a closed subspace M of H is invariant under both T and T*, then M is called a reducing subspace of T on H. Reducing subspaces of the multiplication operator M_B on the Hardy and Bergman spaces have been studied extensively in the past, where B is a finite Blaschke product. This topic lies at the intersection of complex analysis, operator theory, operator algebra, Riemann surface, and group theory and so on, reflecting a rich interplay among these areas. In this talk, we will review some key results concerning reducing subspaces on the Hardy and Bergman spaces. We will also discuss some questions related to the group-theoretic aspects of reducing subspaces on the Bergman space.