A Radon-Nikodym type theorem for $\alpha$-completely positive maps on groups
Operator Algebras
2013-08-08 v1 Functional Analysis
Abstract
We show that an operator valued -completely positive map on a group G is given by a unitary representation of G on a Krein space which satisfies some condition. Moreover, two unitary equivalent such unitary representations define the same {\alpha}-completely positive map. Also we introduce a pre-order relation on the collection of {\alpha}-completely positive maps on a group and we characterize this relation in terms of the unitary representation associated to each map.
Cite
@article{arxiv.1308.1498,
title = {A Radon-Nikodym type theorem for $\alpha$-completely positive maps on groups},
author = {Maria Joiţa},
journal= {arXiv preprint arXiv:1308.1498},
year = {2013}
}