可控算子对的谱配置问题

On the spectrum assignment probelm for the controllable operator pairs

设(?)和(?)为复Hiblert空间,给定算子A∈(?)((?)),B∈(?)((?))。当算子对(A,B)是可控算子对时,通过空间分解、极分解及构造算子矩阵的技巧,利用数学归纳法给出著名谱配置定理的一个比较清晰的证明,然后给出这个定理的一个应用.

Given the operators A, B with A, B acting on complex Hilbert spaces H and K, respectively. Firstly,using the space decomposition, the polar decomposition and the constuction technique in operator matrix, a clear proof is given for the well known spectrum assignment theorem by the mathematical induction when the pair operator （A, B） is controllable. Secondly, an application is obtained for this theory.