Geodesic
Moore–Penrose inverses of Gram operators on Hilbert $C^*$-modules
M. S. Moslehian1 ; K. Sharif2 ; M. Forough3 ; M. Chakoshi4
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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 
@article{10_4064_sm210_2_6,
     author = {M. S. Moslehian and K. Sharif and M. Forough and M. Chakoshi},
     title = {Moore{\textendash}Penrose inverses of {Gram} operators on {Hilbert} $C^*$-modules},
     journal = {Studia Mathematica},
     pages = {189--196},
     publisher = {mathdoc},
     volume = {210},
     number = {2},
     year = {2012},
     doi = {10.4064/sm210-2-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm210-2-6/}
}
TY  - JOUR
AU  - M. S. Moslehian
AU  - K. Sharif
AU  - M. Forough
AU  - M. Chakoshi
TI  - Moore–Penrose inverses of Gram operators on Hilbert $C^*$-modules
JO  - Studia Mathematica
PY  - 2012
SP  - 189
EP  - 196
VL  - 210
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm210-2-6/
DO  - 10.4064/sm210-2-6
LA  - en
ID  - 10_4064_sm210_2_6
ER  - 
%0 Journal Article
%A M. S. Moslehian
%A K. Sharif
%A M. Forough
%A M. Chakoshi
%T Moore–Penrose inverses of Gram operators on Hilbert $C^*$-modules
%J Studia Mathematica
%D 2012
%P 189-196
%V 210
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm210-2-6/
%R 10.4064/sm210-2-6
%G en
%F 10_4064_sm210_2_6
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

Cité par Sources :