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