Characterizations and representations for the Drazin inverse of anti-triangular block operator matrices with index less than two
Chuj an Lin, Xia li Deng, Chunyan Deng · Operators and Matrices · 2021
In the 1980s, Campbell proposed a problem to find an expression of the Drazin inverse for the block matrix A B -I 0 to research on singular differential equations. In this paper, some characterizations and detail representations for the Drazin inverse of anti-triangular block operator matrices M = A B I 0 with ind(M) = 1 ( resp. ind(M) = 2 ) are given.