【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.更多还原

【Abstract】 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]>n²-2n+2, then T must be Hilbert irreducible.更多还原