| Unitary Equivalence, Similarity and Calculation of K0-Group |
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| 引用本文： | Hua HE Chun Lan JIANG. Unitary Equivalence, Similarity and Calculation of K0-Group[J]. 数学学报(英文版), 2005, 21(6): 1259-1268. DOI: 10.1007/s10114-004-0461-9 |
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| 作者姓名： | Hua HE Chun Lan JIANG |
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| 作者单位： | [1]Department of Applied Mathematics, Hebei University of Technology, Tianjin, 300130, P. R. China [2]Academy of Mathematics and Systems Science, Chinese Academy of Science,Beijing, 100080, P. R. China |
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| 基金项目： | This work is supported by the 973 Project of China, and the National Natural Science Foundation of China （Grant No, 19631070） |
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| 摘 要： | In this paper, we are concerned with the classification of operators on complex separable Hilbert spaces, in the unitary equivalence sense and the similarity sense, respectively. We show that two strongly irreducible operators A and B are unitary equivalent if and only if W＊（A＋B）′≈M2（C）, and two operators A and B in B1（Ω） are similar if and only if A′（AGB）/J≈M2（C）. Moreover, we obtain V（H^∞（Ω,μ）≈N and Ko（H^∞（Ω,μ）≈Z by the technique of complex geometry, where Ω is a bounded connected open set in C, and μ is a completely non-reducing measure on Ω.
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| 关 键 词： | K0群 等价性 相似性 Cowen-Douglas算子 流形 |
| 收稿时间： | 2003-02-26 |
| 修稿时间： | 2003-02-262003-06-19 |
Unitary Equivalence, Similarity and Calculation of K 0–Group |
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| Hua He,Chun Lan Jiang. Unitary Equivalence, Similarity and Calculation of K 0–Group[J]. Acta Mathematica Sinica(English Series), 2005, 21(6): 1259-1268. DOI: 10.1007/s10114-004-0461-9 |
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| Authors: | Hua He Chun Lan Jiang |
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| Affiliation: | (1) Department of Applied Mathematics, Hebei University of Technology, Tianjin 300130, P. R. China;(2) Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100080, P. R. China;(3) Department of Applied Mathematics, Hebei University of Technology, Tianjin 300130, P. R. China |
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| Abstract: | |
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| Keywords: | Strongly irreducible operators Cowen-Douglas operator Holomorphic complex bundle Grassmann manifold K0-group |
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