New results on reverse order law for {1,2,3}- and {1,2,4}-inverses of bounded operators

Liu, Xiaoji; Wu, Shuxia; Cvetković-Ilić, Dragana

doi:10.1090/S0025-5718-2013-02660-9

New results on reverse order law for $\{1,2,3\}$- and $\{1,2,4\}$-inverses of bounded operators
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by Xiaoji Liu, Shuxia Wu and Dragana Cvetković-Ilić

Math. Comp. 82 (2013), 1597-1607

DOI: https://doi.org/10.1090/S0025-5718-2013-02660-9

Published electronically: January 11, 2013

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Abstract:

In this paper, using some block-operator matrix techniques, we give 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, we present some new equivalents of the reverse order law for the Moore-Penrose inverse.

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