Glasnik Matematicki, Vol. 44, No.1 (2009), 187-193.

ON THE ORDER STRUCTURE ON THE SET OF COMPLETELY MULTI-POSITIVE LINEAR MAPS ON C*-ALGEBRAS

Maria Joita, Tania-Luminita Costache and Mariana Zamfir

Faculty of Applied Sciences, University "Politehnica" of Bucharest, Romania
e-mail: lumycos@yahoo.com

Department of Mathematics and Informatics, Technical University of Civil Engineering Bucharest, Romania
e-mail: zamfirvmariana@yahoo.com

Abstract.   In this paper we characterize the order relation on the set of all completely n-positive linear maps on C*-algebras in terms of the representation associated to each completely n-positive linear map given by Suen's construction.

2000 Mathematics Subject Classification.   46L05, 47A20, 47L90.

Key words and phrases.   C*-algebra, completely multi-positive linear map, Radon-Nikodym type theorem, pure completely multi-positive linear map, extremal completely multi-positive linear map.

DOI: 10.3336/gm.44.1.11

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