非线性分块算子矩阵的Dörfner谱性质  

The properties of Dörfner spectrum of nonlinear block operator matrices

作　　者：董小梅 吴德玉[2] DONG Xiaomei;WU Deyu(College of Science,Inner Mongolia University of Technology,Hohhot 010051,China;School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051 [2]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《内蒙古工业大学学报（自然科学版）》2024年第1期1-5,共5页Journal of Inner Mongolia University of Technology：Natural Science Edition

基　　金：内蒙古自治区自然科学基金项目(2023QN01012);内蒙古工业大学科学研究项目(DC2300001264);内蒙古自治区引进人才支持项目(DC2300001432)。

摘　　要：研究了对角非线性分块算子矩阵、上三角非线性分块算子矩阵以及斜对角非线性分块算子矩阵的Dörfner谱,得到了整个算子矩阵的Dörfner谱与其内部元的Dörfner谱之间的关系。此外,利用Frobenius-Schur分解方法,得到了2×2非线性分块算子矩阵的Dörfner谱与其Schur补的Dörfner谱之间的关系。The Dörfner spectrum of diagonal nonlinear block operator matrices,upper triangular nonlinear block operator matrices and off-diagonal nonlinear block operator matrices are studied respectively,and the connections between the Dörfner spectrum of those nonlinear block operator matrices and that of their entries are obtained.Moreover,the relationship between the Dörfner spectrum of 2×2 nonlinear block operator matrices and that of their Schur complement is obtained by Forbenius-Schur decomposition.

关 键 词：非线性算子 算子矩阵 Dörfner谱 

分 类 号：O177.7[理学—数学] O177.92[理学—基础数学]