Additive results for the group inverse in an algebra with applications to block operators

Benítez López Julio, XIAOJI LIU

2011

Linear and Multilinear Algebra

We derive a very short expression for the group inverse of a1+.+an when a1,.an are elements in an algebra having group inverse and satisfying aiaj=0for i<j. We apply this formula in order to find the group inverse of 2×2 block operators under some conditions. © 2011 Taylor & Francis.