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On the structure of the set of positive maps

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Abstract

The full description of the set of positive maps \(T: {\mathfrak {A}}\rightarrow {\mathcal {B}}({\mathcal {H}})\) (\({\mathfrak {A}}\) a \(C^*\)-algebra) is given. The approach is based on the simple prescription for selecting various types of positive maps. This prescription stems from the Grothendieck theory of projective tensor products complemented by the theory of tensor connes. In particular, the origin of non-decomposable maps is clarified.

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Acknowledgements

The author would like to express his thanks to Louis E. Labuschagne and Marcin Marciniak for several helpful comments. Furthermore, he wishes to thank the University of Gdansk where a part of the research was done.

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  1. Unit for BMI, North-West-University, Potchefstroom, South Africa

    W. A. Majewski

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Majewski, W.A. On the structure of the set of positive maps. Positivity 24, 799–813 (2020). https://doi.org/10.1007/s11117-019-00708-x

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