Extension of positive maps
DOI:
https://doi.org/10.7146/math.scand.a-115974Abstract
We prove an extension theorem for positive maps from operator systems into matrix algebras
References
Arveson, W. B., Subalgebras of $C^ast $-algebras, Acta Math. 123 (1969), 141–224. https://doi.org/10.1007/BF02392388
Bhatia, R., Positive definite matrices, Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ, 2007.
Davidson, K. and Paulsen, V., An example of a non-extendible positive map on a subsystem of the matrices, personal communication, 2020.
Paulsen, V., Completely bounded maps and operator algebras, Cambridge Studies in Advanced Mathematics, vol. 78, Cambridge University Press, Cambridge, 2002.
Størmer, E., Extension of positive maps into $B(mathcal H)$, J. Funct. Anal. 66 (1986), no. 2, 235–254. https://doi.org/10.1016/0022-1236(86)90072-8
Størmer, E., Positive linear maps of operator algebras, Springer Monographs in Mathematics, Springer, Heidelberg, 2013. https://doi.org/10.1007/978-3-642-34369-8