The Moore–Penrose inverses of lower triangular operators

Abstract

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].

Keywords:

• Moore–Penrose inverse
• Bott–Duffin inverse

AMS Subject Classifications:

• 47A05
• 15A09

Acknowledgements

The author thanks the referee for valuable suggestions. The work was supported by the Project of Excellence Pre-Research in Technology of Shaanxi Normal University. This subject is supported by NSF of China (No: 10871224), and also the Fundamental Research Funds for the Central Universities (GK200902049).