Classification of quasi-homogeneous holomorphic curves and operators in the Cowen-Douglas class
Classification of quasi-homogeneous holomorphic curves and operators in the Cowen-Douglas class
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Cowen-Douglas 类中准齐次全纯曲线和算子的分类
DOI：
10.1016/j.jfa.2017.06.015
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发表时间：
2017
影响因子：
1.7
通讯作者：
Misra Gadadhar
中科院分区：
文献类型：
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作者：
Jiang Chunlan;Ji Kui;Misra Gadadhar
本文研究Cowen-Douglas类中的拟齐次算子，其中包括齐次算子。我们给出了两个独立的定理描述典型的模型（关于等价下的酉和可逆的运营商，分别），这些运营商使用复杂的几何技术。这大大推广了最近作者和A.科拉尼在齐次算子的性质的一个重要推广中，我们证明了拟齐次算子是不可约的，并确定了它们中哪些是强不可约的。应用包括一个准齐次算子的拓扑和代数K-群的等式和一个著名的Halmos问题的肯定答案。
In this paper we study quasi-homogeneous operators, which include the homogeneous operators, in the Cowen–Douglas class. We give two separate theorems describing canonical models (with respect to equivalence under unitary and invertible operators, respectively) for these operators using techniques from complex geometry. This considerably extends the similarity and unitary classification of homogeneous operators in the Cowen–Douglas class obtained recently by the last author and A. Korányi. In a significant generalization of the properties of the homogeneous operators, we show that quasi-homogeneous operators are irreducible and determine which of them are strongly irreducible. Applications include the equality of the topological and algebraicK-group of a quasi-homogeneous operator and an affirmative answer to a well-known question of Halmos.