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This paper mainly concerns a tuple of multiplication operators
defined on the weighted and unweighted multi-variable Bergman
spaces, their joint reducing subspaces and the von Neumann algebra
generated by the orthogonal projections onto these subspaces. It is
found that the weights play an important role in the structures of
lattices of joint reducing subspaces and of associated von Neumann
algebras. Also, a class of special weights is taken into account.
Under a mild condition it is proved that if those multiplication
operators are defined by the same symbols, then the corresponding
von Neumann algebras are $*$-isomorphic to the one defined on the
unweighted Bergman space. 相似文献
2.
Wolfgang Knirsch 《Mathematische Nachrichten》2002,245(1):94-103
On bounded pseudoconvex domains Ω the orthogonal projection Pq : L2(p,q) (Ω) → ker q is given by Pq = Id – Sq+1 q = Id – *q+1Nq+1 q, where Sq is the canonical solution operator of the ‐equation and Nq is the ‐Neumann operator. We prove a formula for the solution operator Sq restricted on (0, q)‐forms with holomorphic coefficients. And as an application we get a characterization of compactness of the solution operator restricted on (0, q)‐forms with holomorphic coefficients. On general (0, q)‐forms we show that this condition is necessary for compactness of the solution operator. 相似文献
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