Geodesic
Moore–Penrose inverses of Gram operators on Hilbert $C^*$-modules
M. S. Moslehian1 ; K. Sharif2 ; M. Forough3 ; M. Chakoshi4
1Department of Pure Mathematics Center of Excellence in Analysis on Algebraic Structures (CEAAS) Ferdowsi University of Mashhad P.O. Box 1159, Mashhad 91775, Iran
2Department 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
3Department of Mathematics Ferdowsi University of Mashhad P.O. Box 1159, Mashhad, Iran
4Tusi 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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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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