Positive Map

Let A and B be C^*-algebras, then a linear map phi:A->B is said to be positive if phi(A_+) subset= B_+. Here, A_+ is denoted the positive part of A.

For example, every *-homomorphism is positive (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.

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Moslehian, Mohammad Sal. "Positive Map." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PositiveMap.html

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