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Operator matrix of Moore–Penrose inverse operators on Hilbert $C^*$-modules

Volume 140 / 2015

Mehdi Mohammadzadeh Karizaki, Mahmoud Hassani, Maryam Amyari, Maryam Khosravi Colloquium Mathematicum 140 (2015), 171-182 MSC: Primary 46L08; Secondary 15A09, 47A05. DOI: 10.4064/cm140-2-2

Abstract

We show that the Moore–Penrose inverse of an operator $T$ is idempotent if and only if it is a product of two projections. Furthermore, if $P$ and $Q$ are two projections, we find a relation between the entries of the associated operator matrix of $PQ$ and the entries of associated operator matrix of the Moore–Penrose inverse of $PQ$ in a certain orthogonal decomposition of Hilbert $C^*$-modules.

Authors

  • Mehdi Mohammadzadeh KarizakiDepartment of Mathematics
    Mashhad Branch, Islamic Azad University
    Mashhad 91735, Iran
    e-mail
  • Mahmoud HassaniDepartment of Mathematics
    Mashhad Branch, Islamic Azad University
    Mashhad 91735, Iran
    e-mail
  • Maryam AmyariDepartment of Mathematics
    Mashhad Branch, Islamic Azad University
    Mashhad 91735, Iran
    e-mail
  • Maryam KhosraviFaculty of Mathematics and Computer Science
    Shahid Bahonar University of Kerman
    Kerman, Iran
    and
    Tusi Mathematical Research Group
    (TMRG)
    P.O. Box 1113
    Mashhad 91775, Iran
    e-mail

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