All 2-positive linear maps from M3(C) to M3(C) are decomposable

All 2-positive linear maps from M3(C) to M3(C) are decomposable Following an idea of Choi, we obtain a decomposition theorem for k-positive linear maps from Mm(C) to Mn(C), where 2≤k<min⁡{m,n}. As a consequence, we give an affirmative answer to Kye's conjecture (also solved independently by Choi) that every 2-positive linear map from M3(C) to M3(C) is decomposable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Linear Algebra and its Applications Elsevier

All 2-positive linear maps from M3(C) to M3(C) are decomposable

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Publisher
Elsevier
Copyright
Copyright © 2016 Elsevier Inc.
ISSN
0024-3795
eISSN
1873-1856
D.O.I.
10.1016/j.laa.2016.03.050
Publisher site
See Article on Publisher Site

Abstract

Following an idea of Choi, we obtain a decomposition theorem for k-positive linear maps from Mm(C) to Mn(C), where 2≤k<min⁡{m,n}. As a consequence, we give an affirmative answer to Kye's conjecture (also solved independently by Choi) that every 2-positive linear map from M3(C) to M3(C) is decomposable.

Journal

Linear Algebra and its ApplicationsElsevier

Published: Aug 15, 2016

References

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