有关幂等算子的Drazin逆等价性  

The Drazin inverse properties for idempotent operators

作　　者：成立花[1] CHENG Lihua(School of Science,Xi′an Polytechnic University,Xi′an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2019年第1期63-66,共4页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11101323);陕西省科技厅自然科学专项基金(2016JQ1029)

摘　　要：研究Hilbert空间上幂等算子的Drazin逆等价性性质。引入Hilbert空间上有界线性算子的空间分解理论和算子矩阵分块的技巧,给出幂等算子在一定空间分解下的算子矩阵表示,进而研究幂等算子和、差和积的Drazin逆的几个等价条件,最后给出幂等算子积条件下Drazin逆的等价条件。Properties of two idempotent operators on a Hilbert space are studied.Based on the theory of space decomposition of linear and bounded operators and the technique of operator matrix blocking,the representations and characterization of two idempotent operators on a given Hilbert space are given.And several equivalent conditions for the Drazin invertibility of the sum,difference of two idempotents on a Hilbert space are studied.Furthermore,equivalent condition for the Drazin invertibility of the product of idempotents is obtained.

关 键 词：DRAZIN逆 幂等算子 Drazin指数 

分 类 号：O175.25[理学—数学]