New results on reverse order law for $\{1,2,3\}$- and $\{1,2,4\}$-inverses of bounded operators
نویسندگان
چکیده
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 کاملNew results on reverse order law for {1, 2, 3}- and {1, 2, 4}-inverses of bounded operators
In this paper, using some block-operator matrix techniques, we give the necessary and sufficient conditions for the reverse order law for {1, 2, 3} and {1, 2, 4}−inverses of bounded operators on Hilbert spaces. Furthermore, we present new equivalent conditions for the reverse order law for the Moore-Penrose inverse. AMS classification: 15A09
متن کاملFurther Results on the Reverse Order Law for Generalized Inverses
The reverse order rule (AB)† = B†A† for the Moore-Penrose inverse is established in several equivalent forms. Results related to other generalized inverses are also proved.
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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 کاملNew results on the quasi-commuting inverses
A matrix has an ordinary inverse only if it is square, and even then only if it is nonsingular or, inother words, if its columns (or rows) are linearly independent. In recent years needs have been felt innumerous areas of applied mathematics for some kind of partial inverse of a matrix that is singularor even rectangular. In this paper, some results on the Quasi-commuting inverses, are given an...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2013
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2013-02660-9