Abstract
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.
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