@article { author = {Sharifi, K. and A. Bonakdar, Behnaz}, title = {The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {42}, number = {1}, pages = {53-60}, year = {2016}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {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.}, keywords = {Bounded adjointable operator,Hilbert C*-module,generalized inverse,reverse order law}, url = {http://bims.iranjournals.ir/article_741.html}, eprint = {http://bims.iranjournals.ir/article_741_e95e4eb2557dba2d2bb48b970aa22608.pdf} }