Geodesic
Moore–Penrose inverses of Gram operators on Hilbert $C^*$-modules
M. S. Moslehian 1   ; K. Sharif 2   ; M. Forough 3   ; M. Chakoshi 4
1 Department of Pure Mathematics Center of Excellence in Analysis on Algebraic Structures (CEAAS) Ferdowsi University of Mashhad P.O. Box 1159, Mashhad 91775, Iran
2 Department of Mathematics Shahrood University of Technology P.O. Box 3619995161-316, Shahrood, Iran and School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran
3 Department of Mathematics Ferdowsi University of Mashhad P.O. Box 1159, Mashhad, Iran
4 Tusi Mathematical Research Group P.O. Box 1113, Mashhad, Iran
Studia Mathematica, Tome 210 (2012) no. 2, pp. 189-196 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $t$ be a regular operator between Hilbert $C^*$-modules and $t^\dagger$ be its Moore–Penrose inverse. We investigate the Moore–Penrose invertibility of the Gram operator $t^*t$. More precisely, we study some conditions ensuring that $t^{ \dagger} = (t^* t)^{ \dagger} t^*= t^*(t t^*)^{ \dagger}$ and $(t^*t)^{\dagger}=t^{ \dagger}t^{* \dagger}$. As an application, we get some results for densely defined closed operators on Hilbert $C^*$-modules over $C^*$-algebras of compact operators.
DOI : 10.4064/sm210-2-6
Keywords: regular operator between hilbert * modules dagger its moore penrose inverse investigate moore penrose invertibility gram operator *t precisely study conditions ensuring dagger * dagger * * * dagger *t dagger dagger * dagger application get results densely defined closed operators hilbert * modules * algebras compact operators

M. S. Moslehian  1   ; K. Sharif  2   ; M. Forough  3   ; M. Chakoshi  4

1 Department of Pure Mathematics Center of Excellence in Analysis on Algebraic Structures (CEAAS) Ferdowsi University of Mashhad P.O. Box 1159, Mashhad 91775, Iran
2 Department of Mathematics Shahrood University of Technology P.O. Box 3619995161-316, Shahrood, Iran and School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran
3 Department of Mathematics Ferdowsi University of Mashhad P.O. Box 1159, Mashhad, Iran
4 Tusi Mathematical Research Group P.O. Box 1113, Mashhad, Iran 
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     title = {Moore{\textendash}Penrose inverses of {Gram} operators on {Hilbert} $C^*$-modules},
     journal = {Studia Mathematica},
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M. S. Moslehian; K. Sharif; M. Forough; M. Chakoshi. Moore–Penrose inverses of Gram operators on Hilbert $C^*$-modules. Studia Mathematica, Tome 210 (2012) no. 2, pp. 189-196. doi: 10.4064/sm210-2-6

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