Mapping Cones are Operator Systems

Details Mapping Cones are Operator Systems Mapping Cones are Operator Systems

2011-02-10

arxiv.org/abs/1102.2012v2

Mathematics

Operator Algebras

12 pages, minor corrections since v1

Scientific paper

10.1112/blms/bds006

We investigate the relationship between mapping cones and matrix ordered *-vector spaces (i.e., abstract operator systems). We show that to every mapping cone there is an associated operator system on the space of n-by-n complex matrices, and furthermore we show that the associated operator system is unique and has a certain homogeneity property. Conversely, we show that the cone of completely positive maps on any operator system with that homogeneity property is a mapping cone. We also consider several related problems, such as characterizing cones that are closed under composition on the right by completely positive maps, and cones that are also semigroups, in terms of operator systems.

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