Positive Linear Functional
Let A be a C^*-algebra, then a linear functional f on A is said to be positive if it is a positive map, that is f(a)>=0 for all a in A_+.
Every positive linear functional is automatically continuous (Murphy 1990).
This entry contributed by Mohammad Sal Moslehian
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References
Murphy, G. J. C-*-Algebras and Operator Theory. New York: Academic Press, 1990.Referenced on Wolfram|Alpha
Positive Linear FunctionalCite this as:
Moslehian, Mohammad Sal. "Positive Linear Functional." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PositiveLinearFunctional.html