Additive property of Drazin invertibility of elements in a ring
Additive property of Drazin invertibility of elements in a ring
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DOI：
10.1080/03081087.2011.629998
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发表时间：
2012-07
影响因子：
1.1
通讯作者：
Guifen Zhuang;Jianlong Chen;D. Cvetković-Ilić;Yimin Wei
中科院分区：
文献类型：
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作者：
Guifen Zhuang;Jianlong Chen;D. Cvetković-Ilić;Yimin Wei
本文研究了环中元素的Drazin逆的可加性。在交换条件 =ba下，我们证明了a+bis Drazin可逆的充要条件是1 db+aDbis Drazin可逆。给出了Drazin逆(a+b)D在a、ad、bD和(1 +adb)D上的显式表示。此外，同样的性质被Banach代数中的广义Drazin可逆性所继承，并被推广到有界线性算子。
In this article, we investigate additive properties on the Drazin inverse of elements in rings. Under the commutative condition ofab=ba, we show thata+bis Drazin invertible if and only if 1 +aDbis Drazin invertible. Not only the explicit representations of the Drazin inverse (a+b)Din terms ofa,aD,bandbD, but also (1 +aDb)Dis given. Further, the same property is inherited by the generalized Drazin invertibility in a Banach algebra and is extended to bounded linear operators.