反三角挠动矩阵的Mosic-Abyzov逆  

Mosic-Abyzov Inverse of the Anti-triangular Perturbation Matrix

作　　者：金雅妮 陈焕艮 JIN Yani;CHEN Huanyin(School of Mathematics,Hangzhou Normal University,Hangzhou 311121,China)

机构地区：[1]杭州师范大学数学学院,浙江杭州311121

出　　处：《杭州师范大学学报（自然科学版）》2024年第6期643-651,共9页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：浙江省自然科学基金项目(LY21A010018).

摘　　要：文章讨论了Banach代数上反三角挠动矩阵的Mosic-Abyzov可逆性.假设a,b∈A.在b^(+)a=0和bab_(π)=0的条件下,利用Peirce分解证明了a^(+)b^(+)∈M_(2)(A).同时,基于矩阵的加法分解,在b^(2)a=0和abab_(π)=0的条件下,证明了a^(+)b^(+)∈M_(2)(A).进一步地,利用方程ax+1=xbx的可解性,在条件b^(+)a=0和(ab)b_(π)=(ba)b_(π)下证明了a^(+)b^(+)∈M_(2)(A).This paper investigated the Mosic-Abyzov inverse of an anti-triangular perturbation matrix over Banach algebra.Let a,b∈A,under the conditions of b^(+)a=0 and bab_(π)=0,it is proved that a^(+)b^(+)∈M_(2)(A)using the Peirce decomposition.Based on the additive decomposition of matrices,it is also proved that if b^(2)a=0 and abab_(π)=0,then a^(+)b^(+)∈M_(2)(A).Moreover,it is shown that a^(+)b^(+)∈M_(2)(A)if b^(+)a=0 and(ab)b_(π)=(ba)b_(π)by means of the solvability of the equation ax+1=xbx.

关 键 词：Mosic-Abyzov逆 Peirce分解 反三角矩阵 BANACH代数 

分 类 号：O153.3[理学—数学]