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...

The reverse order law and the forward have been studied for various types of generalized inverses. $(b,c)$-inverse is a generalization some well known inverses, such as Moore-Penrose inverse, Drazin core etc. In this paper, $(b,c)$-inverse, in unital ring, investigated an equivalent condition to hold derived. Also, results on topic are generalized. Furthermore, ring with unity introduced, diffe...

We study equivalent conditions for the reverse order law (a1a2 . . . an)† = an(a † 1a1a2 . . . ana † n) †a1 in C ∗-algebras. As corollaries, we obtain some recent and special results.