Group invertibility of the sum in rings and its applications
Abstract
We present new additive results for the group invertibility in a ring. Then we apply our results to block operator matrices over Banach spaces and derive the existence of group inverses of 2× 2 block operator matrices. These generalize many known results, e.g., Benitez, Liu and Zhu(Linear Multilinear Algebra, 59(2011), 279--289) and Zhou, Chen and Zhu(Comm. Algebra, 48(2020),676-690).
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