论文标题
Banach代数中G-Drazin逆的新特征
New characterizations of G-Drazin inverse in Banach algebra
论文作者
论文摘要
在本文中，我们介绍了Banach代数中G-Drazin逆的新特征。我们证明元素A是Banach代数的，并且仅当存在$ x \时，$ x \ in $ xa = xa = xa，a-a^2x \ in A^{qnil} $。我们为在Banach代数上以某些$ 2 $ 2 $抗三角形矩阵的某些$ 2 \ times times times 2 $抗triangular矩阵获得了足够和必要的条件。这些扩展了Koliha的结果（GlasgowMath。J.，38（1996），367-381），Nicholson（Comm。Algebra，27（1999），3583-3592和Zou等人（StudiaScient。Math。Hungar。，Hungar。，54（2017,489-508）。
In this paper, we present a new characterization of g-Drazin inverse in a Banach algebra. We prove that an element a is a Banach algebra has g-Drazin inverse if and only if there exists $x\in A$ such that $ax=xa, a-a^2x\in A^{qnil}$. we obtain the sufficient and necessary conditions for the existence of the g-Drain inverse for certain $2 \times 2$ anti-triangular matrices over a Banach algebra. These extend the results of Koliha (Glasgow Math. J., 38(1996), 367-381), Nicholson (Comm. Algebra,27(1999), 3583-3592 and Zou et al. (Studia Scient. Math. Hungar., 54(2017,489-508).
