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The representation and computational procedures for the generalized inverse \(A_{T,S}^{(2)}\) of an operator \(A\) in Hilbert spaces. (English) Zbl 1165.47004

In this paper, the authors present characterizations of the \(A^{(2)}_{T,S}\) generalized inverse of a bounded linear operator \(A\) in Hilbert spaces and over Banach spaces. For the case of Hilbert spaces, some computational procedures are presented in order to obtain the generalized inverse \(A^{(2)}_{R(G),N(G)}\) and their error bound, with \(R(G)\) and \(N(G)\) denoting the range and null space of the operator \(G\).

MSC:

47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
15A09 Theory of matrix inversion and generalized inverses
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