Proper splitting for the generalized inverse \(A^{(2)}_{T, S}\) and its application on Banach spaces. (English) Zbl 1252.47001

Liu, Xiaoji; Huang, Shaowu

Abstr. Appl. Anal. 2012, Article ID 736929, 9 p. (2012).

Summary: A possible type of the operator splitting is studied. Using this operator splitting, we introduce some properties and representations of generalized inverses as well as an iterative method for computing various solutions of the restricted linear operator system \(Ax = b\), \(x \in T\), where \(A \in \mathcal L(X, Y)\) and \(T\) is an arbitrary but fixed subspace of \(X\).

MSC:

47A05	General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47A50	Equations and inequalities involving linear operators, with vector unknowns

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