Cowen-Douglas算子的一些注记  

Some Remarks on Cowen-Douglas Operators

作　　者：曹阳[1] 

机构地区：[1]吉林大学数学学院数学系,长春130012

出　　处：《吉林大学学报（理学版）》2005年第1期1-4,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10371049).

摘　　要：取定Cowen Douglas算子T∈Bn(Ω),给出了其对应的复解析丛ET的一类特殊截面,进而引入Cowen Douglas算子一类新的更易计算的酉不变量[Φ].在n≥2的情形,[Φ]是n×n的复光滑函数值矩阵Φ(T)的对合等价类,特别地,在B1(Ω)的情形,其为实值函数.在此基础上,给出一类Cowen Douglas算子的分解惟一性.证明了当一个Cowen Douglas算子T满足D[Φ]>n2-2n+2时,T是Hilbert不可约的.For a given Cowen-Douglas operator T∈B_n(Ω), a special kind of cross-sections of the corresponding complex bundle E_T is presented. A new unitary invariant [Φ] is introduced, which is the conjugate classes of the complex C~∞ function valued n×n matrix Φ(T) in the case of n≥2 and a real function in the case of n=1. For a given matrix Φ(T)=(φ_(ij))∈[Φ], let F=∨ni,j=1｛φ_(ij)｝. dim Fis independent of the choice of (Φ(T)). Define D[Φ]=dim F. By a discussion on the behavior of (D[Φ]), we show the uniqueness of a special kind of Cowen-Douglas operators. Moreover, we have proved that if a Cowen-Douglas operator T∈B_n(Ω) satisfies D[Φ]>n^2-2n+2, then T must be Hilbert irreducible.

关 键 词：COWEN-DOUGLAS算子 酉不变量 复厄米特解析向量丛 Hilbert约化 约化分解惟一 性 

分 类 号：O177.1[理学—数学]