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C^*-Algebra

A C^*-algebra is a Banach algebra with an antiautomorphic involution * which satisfies

(x^*)^*=x
(1)
x^*y^*=(yx)^*
(2)
x^*+y^*=(x+y)^*
(3)
(cx)^*=c^_x^*,
(4)

where c^_ is the complex conjugate of c, and whose norm satisfies

||xx^*||=||x||^2.
(5)

See also

K-Theory, Pre-C-*-Algebra

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References

Cuntz, J. and Echterhoff, S. (Eds.). C-* Algebras: Proceedings of the SFB-Workshop on C-* Algebras, Münster, Germany, March 8-12, 1999. Berlin: Springer-Verlag, 2000.Davidson, K. R. C-*-Algebras by Example. Providence, RI: Amer. Math. Soc., 1996.Wegge-Olsen, N. E. K-Theory and C-*-Algebras: A Friendly Approach. Oxford, England: Oxford University Press, 1993.

Cite this as:

Weisstein, Eric W. "C^*-Algebra." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/C-Star-Algebra.html

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