Splittings of Operators and Generalized Inverses
نویسندگان
چکیده
In this paper we extend the notion of the proper splitting of rectangular matrices introduced and investigated in ( Berman, A. and Neumann, M., SIAM J. Appl. Math. 31 (1976), 307–312; and Berman, A. and Plemmons, R. J., SIAM J. Numer. Anal. 11 (1974), 145–154) to g-invertible operators on Banach spaces. Also, we extend and generalize the notion of the index splitting of square matrices introduced and investigated in (Wei, Y., Appl. Math. Comput., 95, (1998), 115–124) introducing the {T, S}splitting for arbitrary operators on Banach spaces. The index splitting is a partial case of {T, S}-splitting. The obtained results extend and generalize various well-known results for square and rectangular complex matrices.
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 کاملGeneralized inverses in certain Banach algebras of operators∗
Let X be a Banach space and T be a bounded linear operator from X to itself (T ∈ B(X).) An operator S ∈ B(X) is a generalized inverse of T if TST = T . In this paper we look at several Banach algebras of operators and characterize when an operator in that algebra has a generalized inverse that is also in the algebra. Also, Drazin inverses will be related to generalized inverses and spectral pro...
متن کاملOn the product of projectors and generalized inverses
We consider generalized inverses of linear operators on arbitrary vector spaces and study the question when their product in reverse order is again a generalized inverse. It turns out that this problem is equivalent to the question when the product of projectors is again a projector, and we discuss necessary and sufficient conditions in terms of the defining spaces. We present a new representat...
متن کاملOperators with equal projections related to their generalized inverses
In this article we characterize operators on Banach spaces which have the same projections related to their outer or inner generalized inverses. As corollaries, we obatin well-known results for the Drazin inverse of bounded operators.
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 کامل