Further results on the Moore–Penrose invertibility of projectors and its applications

Abstract

The aim of this article is to investigate new results on the Moore–Penrose invertibility of the products and differences of projectors and generalized projectors. The range relations of projectors and the detailed representations for Moore–Penrose inverses are presented.

Keywords:

• Moore–Penrose inverse
• idempotent
• generalized projector
• range

AMS Subject Classifications::

• 15A09
• 47A10
• 47A55

Acknowledgements

We would like to thank Prof Ravindra Bapat and the referees for their very detailed comments and valuable suggestions which greatly improved our presentation. Chunyuan Deng appreciates Professors Don Hadwin and Hongke Du for their useful discussions. Chunyuan Deng was supported by the Doctoral Program of the Ministry of Education under grant no. 20094407120001. Y. Wei was supported by the National Natural Science Foundation of China under grant no. 10871051, Shanghai Municipal Education Committee (Dawn Project) and Doctoral Program of the Ministry of Education under grant no. 20090071110003.