The structure of invariant alpha-CP multilinear maps and associated J-representations

Abstract

In this paper, we introduce a notion of -completely positive multilinear maps as a generalization of completely positive multilinear maps. We construct a Krein space representation associated with an invariant -completely positive multilinear map and show that the natural ordering of invariant -completely positive multilinear maps is characterized in terms of the Radon–Nikodým derivatives. Finally, we construct a covariant Krein space representation associated with covariant and invariant -completely positive multilinear maps and show that a covariant and invariant -completely positive multilinear map on -algebras can be extended to an -completely positive multilinear map on -crossed products.