A bounded left approximate identity for a normed algebra 
is a bounded net 
with the property 
for 
. Bounded right and two-sided approximate identities are
defined similarly.
Bounded Left Approximate Identity
This entry contributed by Mohammad Sal Moslehian
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References
Bonsall, F. F. and Duncan, J. Complete Normed Algebras. New York: Springer-Verlag, 1973.Referenced on Wolfram|Alpha
Bounded Left Approximate IdentityCite this as:
Moslehian, Mohammad Sal. "Bounded Left Approximate Identity." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/BoundedLeftApproximateIdentity.html