A positive linear functional 
on a C*-algebra 
is a linear functional that is a positive
map, that is 
for all 
, where 
is the set of positive
elements in 
.
Every positive linear functional is automatically continuous (Murphy 1990).
Positive Linear Functional
See also
Operator Algebra State, Quasitrace, Tracial StateThis entry contributed by Mohammad Sal Moslehian
Explore with Wolfram|Alpha
References
Murphy, G. J. C*-Algebras and Operator Theory. New York: Academic Press, 1990.Referenced on Wolfram|Alpha
Positive Linear FunctionalCite this as:
Weisstein, Eric W., with contributions by Mohammad Sal Moslehian. "Positive Linear Functional." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PositiveLinearFunctional.html