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arXiv · 1403.6510

The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules

Kamran Sharifi·Behnaz Ahmadi Bonakdar
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Abstract

Suppose $T$ and $S$ are bounded adjointable operators between Hilbert C*-modules admitting bounded Moore-Penrose inverse operators. Some necessary and sufficient conditions are given for the reverse order law $(TS)^{ †} =S^{ †} T^{ †}$ to hold. In particular, we show that the equality holds if and only if $Ran(T^{\ast}TS) \subseteq Ran(S)$ and $Ran(SS^{\ast}T^{\ast}) \subseteq Ran(T^{\ast}),$ which was studied first by Greville [{\it SIAM Rev. 8 (1966) 518--521}] for matrices.

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Kamran Sharifi, Behnaz Ahmadi Bonakdar. 2014-03-25. The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules. https://arxiv.org/abs/1403.6510

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