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

Authors

  • Behnaz A. Bonakdar Department of‎ ‎Mathematics‎, ‎International Campus of Ferdowsi University‎, ‎Mashhad‎, ‎Iran.
  • K. Sharifi Department of Mathematics, Shahrood University of Technology, and, Mathematisches Institut, Fachbereich Mathematik und Informatik der Universitat Munster, Einsteinstrasse 62, 48149 Munster, Germany.
Abstract:

Suppose $T$ and $S$ are Moore-Penrose invertible operators betweenHilbert C*-module. Some necessary and sufficient conditions are given for thereverse 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.

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Journal title

volume 42  issue 1

pages  53- 60

publication date 2016-02-01

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