Reverse order laws for {1,3,4}-generalized inverses in C∗-algebras

In this paper, we consider the reverse order laws for {1,3,4}-generalized inverses in C∗ algebras. We present purely algebraic necessary and sufficient conditions for b{1,3,4}⋅a{1,3,4}⊆(ab){1,3,4} and (ab){1,3,4}=b{1,3,4}⋅a{1,3,4}. Also, we prove that (ab){1,3,4}⊆b{1,3,4}⋅a{1,3,4} is actually equivalent to (ab){1,3,4}=b{1,3,4}⋅a{1,3,4}.