%0 Journal Article
%T The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Sharifi, K.
%A A. Bonakdar, Behnaz
%D 2016
%\ 02/01/2016
%V 42
%N 1
%P 53-60
%! The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules
%K Bounded adjointable operator
%K Hilbert C*-module
%K generalized inverse
%K reverse order law
%R
%X Suppose $T$ and $S$ are Moore-Penrose invertible operators betweenHilbert C*-module. Some necessary and sufficient conditions are given for thereverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold.In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966) 518--521}] for matrices.
%U http://bims.iranjournals.ir/article_741_e95e4eb2557dba2d2bb48b970aa22608.pdf