Let 
be a T2-topological space and let 
be the space of all bounded complex-valued continuous functions
defined on 
.
The supremum norm is the norm defined on F by
 |
Then 
is a commutative Banach algebra with identity.
Supremum Norm
See also
Norm, SupremumPortions of this entry contributed by José Carlos Santos
Portions of this entry contributed by John Derwent
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References
Taylor, A. E. and Lay, D. C. Introduction to Functional Analysis, 2nd ed. New York: Wiley, 1980.Referenced on Wolfram|Alpha
Supremum NormCite this as:
Weisstein, Eric W., with contributions by José Carlos Santos and John Derwent. "Supremum Norm." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SupremumNorm.html