Voir la notice de l'article provenant de la source Math-Net.Ru
@article{IVM_2012_12_a4, author = {I. N. Maliev and M. A. Pliev}, title = {A {Stinespring} type representation for operators in {Hilbert} modules over local $C^\star$-algebras}, journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika}, pages = {51--58}, publisher = {mathdoc}, number = {12}, year = {2012}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/IVM_2012_12_a4/} }
TY - JOUR AU - I. N. Maliev AU - M. A. Pliev TI - A Stinespring type representation for operators in Hilbert modules over local $C^\star$-algebras JO - Izvestiâ vysših učebnyh zavedenij. Matematika PY - 2012 SP - 51 EP - 58 IS - 12 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IVM_2012_12_a4/ LA - ru ID - IVM_2012_12_a4 ER -
%0 Journal Article %A I. N. Maliev %A M. A. Pliev %T A Stinespring type representation for operators in Hilbert modules over local $C^\star$-algebras %J Izvestiâ vysših učebnyh zavedenij. Matematika %D 2012 %P 51-58 %N 12 %I mathdoc %U http://geodesic.mathdoc.fr/item/IVM_2012_12_a4/ %G ru %F IVM_2012_12_a4
I. N. Maliev; M. A. Pliev. A Stinespring type representation for operators in Hilbert modules over local $C^\star$-algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 51-58. http://geodesic.mathdoc.fr/item/IVM_2012_12_a4/
[1] Kaplansky I., “Modules over operator algebras”, Amer. J. Math., 75 (1953), 839–858 | DOI | MR | Zbl
[2] Manuilov V. M., Troitskii E. V., $C^\star$-gilbertovy moduli, Faktorial, M., 2001
[3] Lance E. C., Hilbert $C^\star$-modules. A toolkit for operator algebraists, Cambridge University Press, 1995 | MR | Zbl
[4] Apostol C., “$b^\star$-algebras and their representations”, J. London Math. Soc., 3 (1971), 30–38 | DOI | MR | Zbl
[5] Inoue A., “Locally $C^\star$-algebras”, Mem. Faculty. Sci. Kyushu. Univ. Ser. A, 25 (1971), 197–235 | DOI | MR | Zbl
[6] Phillips C., “Inverse limits of $C^\star$-algebras”, J. Operator Theory, 19 (1988), 159–195 | MR | Zbl
[7] Joita M., Hilbert modules over locally $C^\star$-algebras, University of Bucharest Press, 2006
[8] Nielsen M. A., Chuang I. L., Quantum computation and quantum information, Cambridge Iniversity Press, 2000 | MR
[9] Stinespring F., “Positive functions on $C^\star$-algebras”, Proc. Amer. Math. Soc., 2 (1955), 211–216 | MR
[10] Kasparov G. G., “Hilbert $C^\star$-modules: The theorems of Stinespring and Voiculescu”, J. Operator Theory, 4 (1980), 133–150 | MR | Zbl
[11] Joita M., “Hilbert modules over locally $C^\star$-algebras: theorem of Stinespring”, Math. Rep. (Bucur.), 53:3 (2001), 21–27 | MR | Zbl
[12] Asadi M. D., “Stinespring's theorem for Hilbert $C^\star$-modules”, J. Operator Theory, 62:2 (2009), 235–238 | MR | Zbl
[13] Bhat R., Ramesh G., Sumesh K., Stinespring's theorem for maps on Hilbert $C^\star$-modules, Preprint, arXiv: 1001.3743
[14] Merfi D., $C^\star$-algebry i teoriya operatorov, Faktorial, M., 1997
[15] Fragoulopoulou M., Topological algebras with involution, Elsevier, 2005 | MR | Zbl
[16] Mallios A., Topological algebras: Selected topics, North-Holland Publishing Company, 1986 | MR | Zbl