Drazin inverses of products and differences of orthogonal projections
Guoxing Ji · Journal of Baoji University of Arts and Sciences · 2007
Let P and Q be two orthogonal projections on a Hilbert space with the operator matrix forms.Aim To discuss the Drazin invertibility of products and differences of orthogonal projections on a Hilbert space,and give the necessary and sufficient conditions for PQ(respectively,P-Q) has the Dazin inverse.Methods The technique of block operator matrices is used to investigate the Drazin invertibility of products and differences of orthogonal projections.Results It is get that PQ(respectively,P-Q) is Drazin invertible if and only if Q0(respectively,I-Q0) is invertible.Meanwhile,the Drazin inverses of PQ and P-Q are established.Conclusion PQ(respectively,P-Q) has the Dazin inverse if and only if PQ(respectively,P-Q) has the Moore-Penrose inverse.