Banach代数中反三角算子矩阵的Hirano逆  

Hirano Inverse of Anti-triangular Operator Matrix in Banach Algebras

作　　者：苟海博 陈焕艮 GOU Haibo;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2期181-188,共8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：文章主要研究Banach代数上反三角算子矩阵的Hirano逆.假设a∈A^(H),b∈A^(sD).如果b^(D)a=0,bab^(π)=0,证明了[a 1 b 0]具有Hirano逆,进而研究了反三角算子矩阵在弱交换条件下的Hirano逆.由此获得了新的可以分解为三幂等元与幂零元和的算子矩阵.This paper investigated Hirano inverse of anti-triangular operator matrix in Banach algebra.Let a∈A^(H),b∈A^(sD).Assuming that b^(D)a=0,bab^(π)=0,it was proven that [a 1 b 0] had Hirano inverse.Moreover,Hirano inverse of anti-triangular operator matrix under certain weak commutative conditions was studied.These results provided a new kind of operator matrix with tripotent and nilpotent decompositions.

关 键 词：Hirano逆 三幂等元 幂零元 BANACH代数 

分 类 号：O153.3[理学—数学]