arXiv:1604.05717

Positive maps which are bijective on the set of rank projections

Erling Størmer

Published Apr 19, 2016• 0 citations

Abstract

Extending Wigner's theorem we give a characterization of positive maps of $B(H)$ into itself which map the set of rank k projections onto itself.

DOI: 10.48550/arxiv.1604.05717

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arXiv:1604.05717

Positive maps which are bijective on the set of rank projections

Erling Størmer

Published Apr 19, 2016• 0 citations

arXiv HTML PDF

Abstract

Extending Wigner's theorem we give a characterization of positive maps of

B(H)

into itself which map the set of rank k projections onto itself.

Extending Wigner's theorem we give a characterization of positive maps of $B(H)$ into itself which map the set of rank k projections onto itself.

DOI: 10.48550/arxiv.1604.05717

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Extending Wigner's theorem we give a characterization of positive maps of

B(H)

into itself which map the set of rank k projections onto itself.

We study mapping cones of positive maps of

B(H)

into itself, i.e., cones which are closed under composition with completely positive maps. As applications we obtain characterizations of linear functionals with strong positivity properties with respect to so-called symmetric mapping cones, with special emphasis on separable and PPT states.