An operator system is a complex linear subspace 
of the bounded operators on a Hilbert
space that contains the identity and is closed under adjoints. It inherits the
positive cones of all matrix spaces 
from 
. Closure under multiplication is not required. For
example, 
is an operator system for any square complex matrix 
(Mohari 2010). A completely
positive map preserves these cones at every matrix size.
Operator System
See also
C*-Algebra, Completely Positive Map, Self-Adjoint ElementExplore with Wolfram|Alpha
References
Mohari, A. "Unital Completely Positive Maps and Their Operator Systems." 27 Jun 2010. https://arxiv.org/abs/1006.5198.Cite this as:
Weisstein, Eric W. "Operator System." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OperatorSystem.html