An approximate unit for a 
-algebra 
is an increasing net 
of positive elements in the closed
unit ball of 
such that 
for all 
in 
or equivalently 
for all 
in 
.
Approximate Unit
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.Referenced on Wolfram|Alpha
Approximate UnitCite this as:
Moslehian, Mohammad Sal. "Approximate Unit." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ApproximateUnit.html