Let T be a Cowen-Douglas operator. In this paper, we study the von Neumann algebra V~*(T) consisting of operators commuting with both T and T~* from a geometric viewpoint. We identify operators in V~*(T) with connection-preserving bundle maps on E(T), the holomorphic Hermitian vector bundle associated to T. By studying such bundle maps, the structure of V~*(T) as well as information on reducing subspaces of T can be determined.
展开▼
