A Radon-Nikodym type theorem for $α$-completely positive maps on groups

Maria Joiţa

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arXiv · 1308.1498

A Radon-Nikodym type theorem for $α$-completely positive maps on groups

Maria Joiţa

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Abstract

We show that an operator valued $α$-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 α-completely positive map. Also we introduce a pre-order relation on the collection of α-completely positive maps on a group and we characterize this relation in terms of the unitary representation associated to each map.

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Maria Joiţa. 2013-08-07. A Radon-Nikodym type theorem for $α$-completely positive maps on groups. https://arxiv.org/abs/1308.1498

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