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W^*-Algebra


A W^*-algebra is a C-*-algebra A for which there is a Banach space A_* such that its dual is A. Then the space A_* is uniquely defined and is called the pre-dual of A. Every von Neumann algebra is a W^*-algebra and vice versa.


See also

von Neumann Algebra

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.Kadison, R. V. and Ringrose, J. R. Fundamentals of the Theory of Operator Algebras, Vol. 2: Advanced Theory. New York: Academic Press, 1986.

Cite this as:

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

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