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| Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces |
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Citation： |
Hansong HUANG,Peng LING.Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces[J].Chinese Annals of Mathematics B,2019,40(2):187~198 |
| Page view： 2145
Net amount： 1262 |
Authors： |
Hansong HUANG; Peng LING |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11471113, 11571064). |
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| Abstract： |
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. |
Keywords： |
Joint reducing subspaces, Von Neumann algebras, Weighted Bergmanspaces |
Classification： |
47A13, 47B35 |
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