Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces
Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces
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DOI：
10.1007/s11401-019-0125-9
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
Han-song Huang;Peng Ling
中科院分区：
文献类型：
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作者：
Han-song Huang;Peng Ling
本文主要研究定义在加权和非加权多变量Bergman空间上的一组乘法算子，它们的联合约简子空间，以及由这些子空间上的正交投影生成的von Neumann代数。研究发现，权值在联合约简子空间和相关的冯·诺伊曼代数的格结构中起着重要的作用。此外，还考虑了一类特殊权重。在温和的条件下，证明了如果这些乘法算子由相同的符号定义，则相应的von Neumann代数与未加权Bergman空间上定义的代数是*-同构的。
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.