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Research articles

ScienceAsia 49 (2023): 43-48 |doi: 10.2306/scienceasia1513-1874.2023.118

Reverse order law for the Moore-Penrose invertible operators on Hilbert C * -modules

Guoqing Hong*

ABSTRACT:      It is well known that an adjointable operator between Hilbert C ? -modules admits a Moore-Penrose inverse if and only if it has closed range. In this paper, we give certain necessary and sufficient conditions for the existence of the reverse order law for the Moore-Penrose inverse of closed range adjointable operators in Hilbert C ? -module settings. Some new related results are also derived, which can be used to establish connections with the reverse order law in Hilbert C ? -modules.

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a Department of Mathematics, Henan Institute of Technology, Xinxiang 453003 China

* Corresponding author, E-mail: guoqinghong@nuaa.edu.cn

Received 24 Mar 2022, Accepted 18 Jun 2022