Operator theory in the Hardy space over the bidisk (II)
Operator theory in the Hardy space over the bidisk (II)
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DOI：
10.1007/bf01203024
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发表时间：
2002
影响因子：
0.8
通讯作者：
Rongwei Yang
中科院分区：
文献类型：
--
作者：
Rongwei Yang
本文是H_2（D_2）中系统算子理论发展项目的继续。它的很大一部分是致力于研究赋值算子，这是一个非常有用的工具，在理论。展示了评价算子的一些基本性质，并且这些性质被用来导出其他主题的结果，例如H2（D2）中特征算子函数的解释，谱等价，紧性，移位算子的压缩等，虽然有些结果反映了H2（D2）的二元性质，但本文的目的是揭示H2（D2）中的算子理论与经典单算子理论之间的密切联系。有限重数的单边移位和Bergman移位将被用作例子来说明一些结果。
This paper is a continuation of a project of developing a systematic operator theory inH2(D2). A large part of it is devoted to a study ofevaluation operatorwhich is a very useful tool in the theory. A number of elementary properties of the evaluation operator are exhibited, and these properties are used to derive results in other topics such as interpretation of characteristic opertor function inH2(D2), spectral equivalence, compactness, compressions of shift operators, etc., Even though some results reflect the two variable nature ofH2(D2), the goal of this paper is to manifest a close tie between the operator theory inH2(D2) and classical single operator theory. The unilateral shift of a finite multiplicity and the Bergman shift will be used as examples to illustrate some of the results.