The Moore–Penrose inverses of lower triangular operators
Yuanli Cai · Linear and Multilinear Algebra · 2011
In this article, we give some necessary and sufficient conditions under which the Moore–Penrose inverse of a lower triangular operator has the lower and upper triangular forms, respectively. As a special case, we recover some theorems and corollaries of Chen et al. [Perturbation analysis of the generalized Bott–Duffin inverse of L-zero matrices, Linear Multilinear Algebra 51 (2003), pp. 11–20] and Deng and Chen [A note on the generalized Bott–Duffin inverse, Appl. Math. Lett., 20 (2007), pp. 746–750].