Further results on the reverse order law for the Moore-Penrose inverse in rings with involution
نویسندگان
چکیده
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.
منابع مشابه
The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules
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...
متن کاملMoore–Penrose inverse in rings with involution
We study the Moore–Penrose inverse (MP-inverse) in the setting of rings with involution. The results include the relation between regular, MPinvertible and well-supported elements. We present an algebraic proof of the reverse order rule for the MP-inverse valid under certain conditions on MP-invertible elements. Applications to C∗-algebras are given. 2000 Mathematics Subject Classification: 46L...
متن کاملSome results on the reverse order law in rings with involution
We investigate some necessary and sufficient conditions for the hybrid reverse order law (ab) = b†a† in rings with involution. Assuming that a and b are Moore-Penrose invertible, we present equivalent condition for the product ab to be EP element.
متن کاملEla Reverse Order Law for the 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.
متن کاملReverse order law for the 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.
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عنوان ژورنال:
- Applied Mathematics and Computation
دوره 218 شماره
صفحات -
تاریخ انتشار 2011