Hilbert-Schmidtness of some finitely generated submodules in H-2 (D-2)
Hilbert-Schmidtness of some finitely generated submodules in H-2 (D-2)
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H-2 (D-2) 中一些有限生成子模块的希尔伯特-施密特性
DOI：
10.1016/j.jmaa.2018.05.021
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发表时间：
2018
影响因子：
1.3
通讯作者：
Yang Rongwei
中科院分区：
文献类型：
--
作者：
Luo Shuaibing;Izuchi Kei Ji;Yang Rongwei
双圆盘上哈代空间H2（D2）的闭子空间M称为子模，如果它在与坐标函数z1和z2相乘时不变。是否每个子模都是Hilbert-Schmidt是一个未解决的问题。本文证明了每一个含有z1 − φ（z2）的n-生成子模M都是Hilbert-Schmidt的，其中φ是任意有限Blaschke积.同时也讨论了一些相关的问题，如条纹算子和Fredholm指数.
A closed subspace M of the Hardy space H 2 (D 2) over the bidisk is called a submodule if it is invariant under multiplication by coordinate functions z 1 and z 2. Whether every finitely generated submodule is Hilbert–Schmidt is an unsolved problem. This paper proves that every finitely generated submodule M containing z 1− φ (z 2) is Hilbert–Schmidt, where φ is any finite Blaschke product. Some other related topics such as fringe operator and Fredholm index are also discussed.