Next: Hilbertian Operator Spaces
Up: Operator Systems and Completely
Previous: Matrix order unit norm
  Contents
  Index
An operator system
is called injectiv if given operator systems
each completely positive map
has a completely positive extension
.
If an operator system
is injective then there is a unital complete order isomorphism from
onto a unital
-algebra. The latter is conditionally complete23.
(cf. [CE77, Theorem 3.1])
Footnotes
- ... complete23
- An ordered vector space
is conditionally complete if any upward directed subset of
that is bounded above has a supremum in
.
Prof. Gerd Wittstock
2001-01-07