Surveys in Mathematics and its Applications


ISSN 1842-6298 (electronic), 1843 - 7265 (print)
Volume 2 (2007), 113 - 122

CHARACTERIZATION OF THE ORDER RELATION ON THE SET OF COMPLETELY n-POSITIVE LINEAR MAPS BETWEEN C*-ALGEBRAS

Maria Joiţa, Tania-Luminiţa Costache and Mariana Zamfir

Abstract. In this paper we characterize the order relation on the set of all nondegenerate completely n-positive linear maps between C*-algebras in terms of a self-dual Hilbert module induced by each completely n-positive linear map.

2000 Mathematics Subject Classification: 46L05; 46L08.
Keywords: Hilbert module, C*-algebra, completely n-positive linear map, extreme points.

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Acknowledgment. This research was supported by CNCSIS grant code A 1065/2006.

References

  1. J. Heo, Completely multi-positive linear maps and representation on Hilbert C*-modules, J. Operator Theory 41 (1999), 3-22. MR1675235(2000a:46103). Zbl 0994.46019.

  2. M. Joiţa, A Radon-Nikodym theorem for completely multi- positive linear maps and its applications, Topological algebras and applications, Contemp. Math. 427 (2007), 235--245. MR2326359. Zbl pre05180876.

  3. M. Joiţa, T.-L. Costache, M. Zamfir, Representations associated with completely n-positive linear maps between C*-algebras, Stud. Cercet. Stiint., Ser. Mat. 16 (2006), Supplement Proceedings of ICMI 45, Bacău, Sept. 18-20, 2006, 111-122. MR2318951.

  4. M. Joiţa, T.-L. Costache, M. Zamfir, On the order structure on the set of completely multi-positive linear maps on C*-algebras (submitted).

  5. E. C. Lance, Hilbert C*-modules. A toolkit for operator algebraists, London Mathematical Society Lecture Note Series 210, Cambridge University Press, Cambridge, 1995. MR1325694(96k:46100). Zbl 0822.46080.

  6. H. Lin, Bounded module maps and pure completely positive maps, J. Operator Theory 26 (1991), 121-139. MR1214924(92h:35103). Zbl 0791.46032.

  7. W. L. Paschke, Inner product modules over B*-algebras, Trans. Amer. Math. Soc. 182 (1973), 443-468. MR0355613(50 #8087). Zbl 0239.46062.

  8. C. Y. Suen, An n ✕ n matrix of linear maps of a C*-algebra, Proc. Amer. Math. Soc. 112 (1991), no.3, 709-712. MR1069296(92a:46069). Zbl 0755.46024.

  9. S. K. Tsui, Completely positive module maps and completely positive extreme maps, Proc. Amer. Math. Soc. 124 (1996), 437-445. MR1301050(96d:46074). Zbl 0846.46037.

Maria Joiţa Tania - Luminita Costache
Department of Mathematics, Faculty of Applied Sciences,
Faculty of Chemistry, University "Politehnica",
University of Bucharest, Bucharest,
Romania. Romania.
e-mail: mjoita@fmi.unibuc.ro e-mail: lumycos@yahoo.com


Mariana Zamfir
Department of Mathematics and Informatics
Technical University of Civil Engineering Bucharest,
Romania.
e-mail: zacos@k.ro

http://www.utgjiu.ro/math/sma