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Positive Element

Let A be a C^*-algebra. An element a in A is called positive if a=a* and sp(a) subset= R^+, or equivalently if there exists an element b in A such that a=bb^*.

For example, the positive elements of the C^*-algebra of complex numbers are the nonnegative real numbers.

The set of all positive elements of A denoted by A_+ is called the positive part of A.

This entry contributed by Mohammad Sal Moslehian

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References

Kadison, R. V. and Ringrose, J. R. Fundamentals of the Theory of Operator Algebras, Vol. 1: Elementary Theory. Providence, RI: Amer. Math. Soc., 1997.Murphy, G. J. C-*-Algebras and Operator Theory. New York: Academic Press, 1990.

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Positive Element

Cite this as:

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

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