关于p群逆的几个新特征

Some New Characterizations of P-group Inverses

本文给出了Banach代数A中的一个元素a有p群逆的新特征,得到了p-Drazin可逆和p群可逆之间的关系.同时讨论了两个p群可逆元素之和是p群可逆的条件,并刻画了Banach代数上2×2矩阵的p群可逆问题.

A new characterization that an element a in a Banach algebra A has p-group inverse was given in this paper,and equivalent conditions for p-Drazin inverse and p-group inverse were obtained.Meantime,the sufficient and necessary conditions for p-group inverse of the sum of two p-group invertible element were discussed,and the existence of p-group inverse of a 2×2 matrix over a Banach algebra was characterized as well.