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arXiv · 1608.00188

Completely semi-$\varphi$-maps

Mohammad B. Asadi·Reza Behmani·Ali R. Medghalchi·Hamed Nikpey
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Abstract

We introduce completely semi-$\varphi$-maps on Hilbert $C^*$-modules as a generalization of $\varphi$-maps. This class of maps provides examples of CP-extendable maps which are not CP-H-extendable, in Skeide-Sumesh's sense. Using the CP-extendability of completely semi-$\varphi$-maps, we give a representation theorem, similar to Stinespring's representation theorem, for this class of maps which can be considered as strengthened and generalized form of Asadi's and Bhat-Ramesh-Sumesh's analogues of Stinespring representation theorem for $\varphi$-maps. We also define an order relation on the set of all completely semi-$\varphi$-maps and establish a Radon-Nikodym type theorem for this class of maps in terms of their representations.

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Mohammad B. Asadi, Reza Behmani, Ali R. Medghalchi, Hamed Nikpey. 2016-07-31. Completely semi-$\varphi$-maps. https://arxiv.org/abs/1608.00188

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