Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591652 | Journal of Functional Analysis | 2011 | 19 Pages |
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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