1,224 research outputs found
Matrix regular operator space and operator system
We establish a relationship between Schreiner's matrix regular operator space
and Werner's (nonunital) operator system. For a matrix ordered operator space
with complete norm, we show that is completely isomorphic and complete
order isomorphic to a matrix regular operator space if and only if both and
its dual space are (nonunital) operator systems.Comment: 8 pages, to appear in JMA
An approximation theorem for nuclear operator systems
We prove that an operator system is nuclear in the category of
operator systems if and only if there exist nets of unital completely positive
maps \phi_\lambda : \cl S \to M_{n_\lambda} and \psi_\lambda : M_{n_\lambda}
\to \cl S such that converges to {\rm
id}_{\cl S} in the point-norm topology. Our proof is independent of the
Choi-Effros-Kirchberg characterization of nuclear -algebras and yields
this characterization as a corollary. We give an example of a nuclear operator
system that is not completely order isomorphic to a unital -algebra.Comment: 10 pages; to appear in JF
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