SPECTRA OF OPERATOR PRODUCTS INVOLVING GENERALIZED INVERSES
Gui-Bao Gao · Xitong kexue yu shuxue · 2009
Let B(H) denote the set of all bounded linear operators on a Hilbert space H. In this note,for three operators A,B and C∈B(H),if the range R(B) of B is closed,then the necessary and sufficient conditions such that σ(AB~(1)C)=C is obtained by using block-operator matrix technique,whereσ(D) is the spectrum of an operator D∈B(H) and B{1}:={X∈B(H):BXB=B}.