Invariance Properties of an Elementary Operator Involving Generalized Inverses
Zuo Ning · International Conference on Electric Information and Control Engineering · 2012
Let B(H) denote the set of all bounded linear operators on a Hilbert space H. In this note, for two operators A, B belong to B(H), if the range R(B) of B is closed, then the necessary and sufficient conditions such that E_A, A^*(B^(1)) does not depend on the choice of B^(1) has been obtained by using block-operator matrix technique, where B^(1)={X\in B(H): BXB=B.