The Representation and Computational Procedures for the Generalized Inverse of an Operator A in Hilbert Spaces

Abstract

In the paper, we present some representations of the generalized inverse over Banach spaces and Hilbert spaces and apply these results to five specific cases to derive specific representations and computational procedures for the generalized inverse of a bounded linear operator in Hilbert spaces and their error bounds. In addition, we give the equivalent conditions for the existence of over Banach spaces.

Keywords:

• Bounded linear operator
• Error bound
• Generalized inverses A_T,S ⁽²⁾
• Representation

AMS Subject Classification:

• 47A05
• 15A09

ACKNOWLEDGMENTS

Y. Yu is supported by the Science Foundation of Shanghai Municipal Education Commission (CW0519). Y. Wei is supported by the National Natural Science Foundation of China under grant 10871051, Shanghai Science and Technology Committee under grant 08DZ2271900, and the Shanghai Education Committee.