A Representation Theorem for Quantum Systems
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 90-96.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this note representations of quantum systems are investigated. We propose a unital bipolar theorem for unital quantum cones, which plays a key role in proving a representation theorem for quantum systems. It turns out that each quantum system is identified with a certain quantum $L^{\infty}$-system up to a quantum order isomorphism.
Keywords: quantum systems, unital quantum cones, quantum $L^{\infty}$-algebra.
@article{FAA_2013_47_3_a8,
     author = {A. A. Dosi},
     title = {A {Representation} {Theorem} for {Quantum} {Systems}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {90--96},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a8/}
}
TY  - JOUR
AU  - A. A. Dosi
TI  - A Representation Theorem for Quantum Systems
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2013
SP  - 90
EP  - 96
VL  - 47
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a8/
LA  - ru
ID  - FAA_2013_47_3_a8
ER  - 
%0 Journal Article
%A A. A. Dosi
%T A Representation Theorem for Quantum Systems
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2013
%P 90-96
%V 47
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a8/
%G ru
%F FAA_2013_47_3_a8
A. A. Dosi. A Representation Theorem for Quantum Systems. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 90-96. http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a8/

[1] N. Burbaki, Obschaya topologiya. Osnovnye struktury, Nauka, M., 1959 | MR

[2] M. D. Choi, E. G. Effros, J. Funct. Anal., 24:2 (1977), 156–209 | DOI | MR | Zbl

[3] A. A. Dosiev, J. Funct. Anal., 255:7 (2008), 1724–1760 | DOI | MR | Zbl

[4] A. A. Dosiev, C. R. Math. Acad. Sci. Paris, 344:10 (2007), 627–630 | DOI | MR | Zbl

[5] A. A. Dosi, Trans. Amer. Math. Soc., 363:2 (2011), 801–856 | DOI | MR | Zbl

[6] A. A. Dosi, J. Math. Phys., 51:6 (2010), 1–43 | DOI | MR

[7] A. A. Dosi, Internat. J. Math., 22:4 (2011), 535–544 | DOI | MR | Zbl

[8] A. Dosi, Funkts. analiz i ego pril., 46:3 (2012), 84–89 | DOI | MR | Zbl

[9] A. A. Dosi, “Quantum cones and their duality”, Houston J. Math. (to appear) | MR

[10] A. A. Dosi, Proc. Amer. Math. Soc., 140:12 (2012), 4187–4202 | DOI | MR | Zbl

[11] E. G. Effros, Z.-J. Ruan, Operator Spaces, Clarendon Press, Oxford, 2000 | MR | Zbl

[12] E. G. Effros, C. Webster, Operator Algebras and Applications (Samos 1996), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 495, Kluwer Acad. Publ., Dordrecht, 1997, 163–207 | MR | Zbl

[13] M. Fragoulopoulou, Yokohama Math. J., 34:1–2 (1986), 35–51 | MR | Zbl

[14] A. Ya. Khelemskii, Kvantovyi funktsionalnyi analiz v beskoordinatnom izlozhenii, MTsNMO, M., 2009

[15] V. Paulsen, Completely bounded maps and operator algebras, Cambridge Studies in Advanced Mathematics, 78, Cambridge University Press, Cambridge, 2002 | MR | Zbl