The generalized inverse has many important applications in aspects of the theoretical research matrices and statistics. One core problems is finding necessary sufficient conditions reverse order laws for operator product. In this paper, we study law g-inverse an product T1T2T3 using technique matrix form bounded linear operators. particular, some inclusion T3{1}T2{1}T1{1} ⊆ (T1T2T3){1} presente...

The reverse order laws for {1,3,4}-generalized inverses of a product of two operators have been studied by Wang et al. [J. Wang, H. Zhang, G. Ji, A generalized reverse order law for the products of two operators, Journal of Shaanxi Normal University, 38 (4) (2010), 13–17]. In this paper using a block-operator matrix technique we study mixed-type reverse-order laws for {1,3,4}-generalized invers...

In this paper, several equivalent conditions related to the reverse order law for the Moore-Penrose inverse in C-algebras are studied. Some well-known results are extended to more general settings. Then this result is applied to obtain the reverse order rule for the weighted Moore-Penrose inverse in C-algebras.

In this paper, several equivalent conditions related to the reverse order law for the Moore-Penrose inverse in C-algebras are studied. Some well-known results are extended to more general settings. Then this result is applied to obtain the reverse order rule for the weighted Moore-Penrose inverse in C-algebras.

We present some equivalent conditions of the reverse order law for the Moore–Penrose inverse in rings with involution, extending some well-known results to more general settings. Then we apply this result to obtain a set of equivalent conditions to the reverse order rule for the weighted Moore-Penrose inverse in C∗-algebras.

In this paper, the necessary and sufficient conditions for reverse order law (AB) #O = B#OA#O are established. addition, hybrid laws (AB)? (AB)# also considered. Text of abstract.