Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces

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
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Authors:

Hansong HUANG; Peng LING

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11471113, 11571064).
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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