A Radon-Nikodym theorem for completely n-positive linear maps on pro-C*-algebras and its applications

Details A Radon-Nikodym theorem for completely n-positive linear maps on pro-C*-algebras and its applications A Radon-Nikodym theorem for completely n-positive linear maps on pro-C*-algebras and its applications

2007-01-09

arxiv.org/abs/math/0701263v1

Mathematics

Operator Algebras

14 pages

Scientific paper

The order relation on the set of completely n-positive linear maps from a pro-C*-algebra A to L(H), the C*-algebra of bounded linear operators on a Hilbert space H, is characterized in terms of the representation associated with each completely n-positive linear map. Also, the pure elements in the set of all completely n-positive linear maps from A to L(H) and the extreme points in the set of unital completely n-positive linear maps from A to L(H) are characterized in terms of the representation induced by each completely n-positive linear map.

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