论文标题
圆环中G-Drazin的广义Cline公式
Generalized Cline's formula for G-Drazin inverse in a ring
论文作者
论文摘要
在本文中，我们为广义Drazin倒数提供了广义的Cline公式。令$ r $为戒指，让$ a，b，c，d \ in R $满足$$ \ begin {array} {c} {c}（ac）^2 =（db）（ac）（ac），（db）^2 =（ac）（db）（db）（db）; \\ b（ac）A = b（db（db）a，c（db）a，c（ac）a，c（ac）$ n = c（ac）$ $ in。 r^d $ if，仅当r^d $中的$ bd \。在这种情况下，$（bd）^d = b（（ac）^d）^2 d $。我们还提出了Cline的广义Cline公式，用于Drazin和Group Inverses。还研究了BANACH代数中一些较弱的条件。这些扩展了Cline公式在LIAO，Chen和Cui逆的G-德拉津的主要结果（Bull。Malays。Math。Soc。，37（2014），37-42，37-42），Lian和Zeng（Turk。J.Math。，40（2016），161-165，161-165），以及Miller and Miller and Miller and Zguitti（rend。 105-114）。作为一种应用，获得了有界线性算子在BANACH空间上的新公共光谱特性。
In this paper, we give a generalized Cline's formula for the generalized Drazin inverse. Let $R$ be a ring, and let $a,b,c,d\in R$ satisfying $$\begin{array}{c} (ac)^2 = (db)(ac), (db)^2 = (ac)(db);\\ b(ac)a = b(db)a, c(ac)d = c(db)d.\end{array}$$ Then $ac\in R^d$ if and only if $bd\in R^d$. In this case, $(bd)^d = b((ac)^d)^2 d$. We also present generalized Cline's formulas for Drazin and group inverses. Some weaker conditions in a Banach algebra are also investigated. These extend the main results of Cline's formula on g-Drazin inverse of Liao, Chen and Cui (Bull. Malays. Math. Soc., 37 (2014), 37-42), Lian and Zeng (Turk. J. Math., 40 (2016), 161-165) and Miller and Zguitti (Rend. Circ. Mat. Palermo, II. Ser., 67 (2018), 105-114). As an application, new common spectral property of bounded linear operators over Banach spaces are obtained.
