Ela Reverse Order Law for the Moore-penrose Inverse in C∗-algebras∗
نویسندگان
چکیده
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.
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...
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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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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.
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In this paper, the special attention is given to the product of two modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented that imply the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved that $P(RPQ)$ is idempotent, if $RPQ$†</...
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تاریخ انتشار 2011