New results on reverse order law for {1, 2, 3}- and {1, 2, 4}-inverses of bounded operators
نویسندگان
چکیده
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
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 کاملMixed-type reverse-order laws for {1, 3, 4}-generalized inverses over Hilbert spaces
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...
متن کاملReverse order laws for {1, 2, 3}-generalized inverses
In this paper, we present purely algebraic necessary and sufficient conditions for reverse order laws for {1, 2, 3} and {1, 2, 4}-generalized inverses on the set of matrices. 2010Mathematics Subject Classification: 15A09
متن کاملEla New Conditions for the Reverse Order Laws for {1, 3} and {1, 4}-generalized Inverses
In this note, the reverse order laws for {1, 3} and {1, 4}-generalized inverses of matrices are considered. New necessary and sufficient conditions for (AB){1, 3} ⊆ B{1, 3} · A{1, 3} and (AB){1, 4} ⊆ B{1, 4} ·A{1, 4} are presented.
متن کاملEla a Note on the Reverse Order Laws for {1, 2, 3}- and {1, 2, 4}-inverses of Multiple Matrix Products
Abstract. Motivated by the equivalent conditions for the inclusions An{1, 2, i} · · ·A2{1, 2, i}A1{1, 2, i} ⊆ (A1A2 · · ·An){1, 2, i} (i = 3, 4) presented in [B. Zheng and Z. Xiong. The reverse order laws for {1,2,3}and {1,2,4}-inverses of multiple matrix products. Linear Multilinear Algebra, 58:765–782, 2010.], we show that for i ∈ {3, 4}, An{1, 2, i} · · ·A2{1, 2, i}A1{1, 2, i} = (A1A2 · · ·A...
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عنوان ژورنال:
- Math. Comput.
دوره 82 شماره
صفحات -
تاریخ انتشار 2013