Abstract
Abstract We present necessary and sufficient conditions under which the sum of two group invertible elements in a ring is group invertible. As applications, we establish the existence of group inverses of certain 2 × 2 {2\times 2} block-operator matrices over a Banach space. These generalize the known results, e.g., Zhou, Chen and Zhu (Comm. Algebra 48 (2020), 676–690) and Benítez, Liu and Zhu (Linear Multilinear Algebra 59 (2011), 279–289).
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