无界分块算子矩阵的可分解性及其应用

The Decomposability of Unbounded Block Operator Matrices and Its Application

无界分块算子矩阵广泛地出现于系统理论、非线性分析以及发展方程问题等领域,在理论和实际应用两方面都受到广泛关注。首先,利用算子局部谱理论得到无界分块算子矩阵可分解性的刻画,其次,给出算子矩阵可分解性保持对角稳定的条件,推广并得到分块算子矩阵在无界情形下的一些局部谱性质。最后,作为应用考察Hamilton算子的可分解性并举例予以说明。

Unbounded block operator matrix widely appears in the elds of system theory,non-linear analysis and evolution equation problems,and has been widely concerned in both theory and practical application.Firstly,the decomposability of unbounded block operator matrix is characterized by using local spectrum theory.Secondly,the condition that the decomposability of operator matrix remains diagonally stable is given,and some local spectral properties of block operator matrix are generalized and obtained.Finally,as an application,the decomposability of Hamilton operator is investigated and illustrated with examples.