1
Department of Mathematics, Shahrood University of Technology, and, Mathematisches Institut, Fachbereich Mathematik und Informatik der Universitat Munster, Einsteinstrasse 62, 48149 Munster, Germany.
2
Department of Mathematics, International Campus of Ferdowsi University, Mashhad, Iran.
Abstract
Suppose $T$ and $S$ are Moore-Penrose invertible operators between Hilbert C*-module. Some necessary and sufficient conditions are given for the reverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold. In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966) 518--521}] for matrices.
Sharifi, K., & A. Bonakdar, B. (2016). The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules. Bulletin of the Iranian Mathematical Society, 42(1), 53-60.
MLA
Sharifi, K., & A. Bonakdar, B. "The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules", Bulletin of the Iranian Mathematical Society, 42, 1, 2016, 53-60.
HARVARD
Sharifi K., A. Bonakdar B. (2016). 'The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules', Bulletin of the Iranian Mathematical Society, 42(1), pp. 53-60.
CHICAGO
K. Sharifi & B. A. Bonakdar, "The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules," Bulletin of the Iranian Mathematical Society, 42 1 (2016): 53-60,
VANCOUVER
Sharifi K., A. Bonakdar B. The reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules. BIMS. 2016;42(1):53-60.
