Unitary Equivalence,Similarity and Calculation of K_0-Group  

作　　者：Hua HE Chun Lan JIANG 

机构地区：[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

出　　处：《Acta Mathematica Sinica,English Series》2005年第6期1259-1268,共10页数学学报（英文版）

基　　金：the 973 Project of China and the National Natural Science Foundation of China(Grant No.19631070)

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.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.

关 键 词：Strongly irreducible operators Cowen-Douglas operator Holomorphic complex bundle Grassmann manifold K0-group 

分 类 号：O152[理学—数学]