反三角算子矩阵的Drazin可逆性及其表示

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英文篇名：The Drazin Inverse and Representation of the Anti-triangular Operator Matrix 作者：韩叶清 ; 王华 英文作者：HAN Yeqing;WANG Hua;College of Sciences,Inner Mongolia University of Technology; 关键词：Drazin逆 ; 预解式 ; Laurent展开 ; 有界线性算子 英文关键词：Drazin inverse;;resolvent;;Laurent expansion;;bounded linear operator 中文刊名：YYFH 英文刊名：Acta Analysis Functionalis Applicata 机构：内蒙古工业大学理学院数学系; 出版日期：2019-03-15 出版单位：应用泛函分析学报 年：2019 期：v.21 基金：国家自然科学基金(11461049,11601249);; 内蒙古自然科学基金(2018MS01002,2017MS0118) 语种：中文; 页：YYFH201901003 页数：13 CN：01 ISSN：11-4016/TL 分类号：37-49

摘要

本文讨论了反三角算子矩阵■的Drazin可逆性及其Drazin逆的表达式.在CB=CAB=CA~2B,A~3=A~2条件下,采用预解式的Laurent展开方法证明了反三角算子矩阵M是Drazin可逆的,并给出M的含有A~D和(CB)~D的Drazin逆的表达式.最后给出算例,说明了结果的有效性.
        In this paper, we study the existence and representation of the Drazin inverse of the anti-triangular operator matrix ■.Based on Laurent expansion method of resolvent, we prove that M is Drazin invertible under the assumptions CB=CAB=CA~2B, A~3=A~2, and the expression of Drazin inverse of M in terms of A~D and (CB)~D is also given. Finally, an example is presented to illustrate the validity of the main result.

引文

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