An order-zero map between C*-algebras 
and 
is a completely positive
map 
that satisfies
 |
whenever 
are positive elements with 
(Winter and Zacharias 2010).
Order-zero maps are used in the definition of nuclear dimension.
Order-Zero Map
See also
C*-Algebra, Completely Positive Map, Nuclear Dimension, Positive ElementExplore with Wolfram|Alpha
References
Winter, W. and Zacharias, J. "The Nuclear Dimension of
-Algebras." Adv. Math. 224,
461-498, 2010. https://doi.org/10.1016/j.aim.2009.12.005.
Cite this as:
Weisstein, Eric W. "Order-Zero Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Order-ZeroMap.html