Decomposability of extremal positive unital maps on $M_2$
Abstract
A map $\phi:M_m(\bC)\to M_n(\bC)$ is decomposable if it is of the form $\phi=\phi_1+\phi_2$ where $\phi_1$ is a CP map while $\phi_2$ is a co-CP map. It is known that if $m=n=2$ then every positive map is decomposable. Given an extremal unital positive map $\phi:M_2(\bC)\to M_2(\bC)$ we construct concrete maps (not necessarily unital) $\phi_1$ and $\phi_2$ which give a decomposition of $\phi$. We also show that in most cases this decomposition is unique.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- September 2005
- DOI:
- 10.48550/arXiv.math/0510005
- arXiv:
- arXiv:math/0510005
- Bibcode:
- 2005math.....10005M
- Keywords:
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- Mathematics - Functional Analysis;
- Mathematics - Operator Algebras;
- 47B65;
- 47L07
- E-Print:
- 9 pages