Approximate Unit
An approximate unit for a C^*-algebra A is an increasing net {u_lambda}_(lambda in Lambda) of positive elements in the closed unit ball of A such that a=lim_(lambda)au_lambda for all a in A or equivalently a=lim_(lambda)u_lambdaa for all a in 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.Referenced on Wolfram|Alpha
Approximate UnitCite this as:
Moslehian, Mohammad Sal. "Approximate Unit." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ApproximateUnit.html