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New results on reverse order law for \(\{1,2,3\}\)- and \(\{1,2,4\}\)-inverses of bounded operators. (English) Zbl 1279.15010

Using some block-operator matrix techniques, the authors establish necessary and sufficient conditions for the reverse order law to hold for \(\{1,2,3\}\)- and \(\{1,2,4\}\)-inverses of bounded operators on Hilbert spaces. Furthermore, the authors present some new equivalents of the reverse order law for the Moore-Penrose inverse.

MSC:

15A09 Theory of matrix inversion and generalized inverses
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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