反三角挠动矩阵的Mosic-Abyzov逆

Mosic-Abyzov Inverse of the Anti-triangular Perturbation Matrix

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.