  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.
