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Multiplication operators on the Bergman space via the Hardy space of the bidisk
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Published/Copyright:
January 21, 2009
Abstract
In this paper, we develop a machinery to study multiplication operators on the Bergman space via the Hardy space of the bidisk. Using the machinery we study the structure of reducing subspaces of a multiplication operator on the Bergman space. As a consequence, we completely classify reducing subspaces of the multiplication operator by a Blaschke product φ with order three on the Bergman space to solve a conjecture of Zhu [J. London Math. Soc. 62: 553–568, 2000].
Received: 2006-08-11
Revised: 2007-12-20
Published Online: 2009-01-21
Published in Print: 2009-March
© Walter de Gruyter Berlin · New York 2009
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Articles in the same Issue
- Groupoids and an index theorem for conical pseudo-manifolds
- Linear forms in elliptic logarithms
- Random quotients of the modular group are rigid and essentially incompressible
- The pro-p Hom-form of the birational anabelian conjecture
- Multiplication operators on the Bergman space via the Hardy space of the bidisk
- Morita equivalences of cyclotomic Hecke algebras of type G(r, p, n)
- Special correspondences and Chow traces of Landweber-Novikov operations
- Double Kodaira fibrations
