Invariance properties of a triple operator product involving generalized inverses
Hong-Ke Du · Journal of Baoji University of Arts and Sciences · 2007
Aim Given three operators A,B and C, the main results obtained by Jurgen Groβ and Yongge Tian in Invariance properties of a triple matrix product involving generalized inverses,([1] Linear Algebra Appl,2006,417: 94-107) are generalized.Methods The proofs in this paper applied the technique of block operator matrix and the idea of solving operator equation.This is different from that by Jurgen Groβ and Yongge Tian.Results Some necessary and sufficient conditions were gotten for the main results in [1] to hold in infinite dimensional Hilbert spaces.Conclusion Certain invariance properties of the triple operator product AXC with respect to the choice of X are established,where X is a different type of generalized inverses of B.