Additive results for the group inverse in an algebra with applications to block operators
Julio Benítez, Xiaoji Liu, Tongping Zhu · Linear and Multilinear Algebra · 2011
We derive a very short expression for the group inverse of a 1 + ··· + a n when a 1, … , a n are elements in an algebra having group inverse and satisfying a i a j = 0 for i < j. We apply this formula in order to find the group inverse of 2 × 2 block operators under some conditions.