%0 Journal Article %T Mapping cones of positive maps %A Erling Stormer %J Mathematics %D 2009 %I arXiv %X This is a revised form of the previous paper in which we study cones of positive maps of B(H) into itself. We add the result that the dual cone of a symmetric mapping cone is itself a symmetric mapping cone. As applications we obtain characterizations of linear functionals with strong positivity conditions with respect to a class of mapping cones called symmetric mapping cones. Applications are given to separable and PPT-states. %U http://arxiv.org/abs/0906.0472v2