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Supremum Norm


Let K be a T2-topological space and let F be the space of all bounded complex-valued continuous functions defined on K. The supremum norm is the norm defined on F by

 ||f||=sup_(x in K)|f(x)|.

Then F is a commutative Banach algebra with identity.


See also

Norm, Supremum

Portions 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 Norm

Cite this as:

Derwent, John; Santos, José Carlos; and Weisstein, Eric W. "Supremum Norm." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SupremumNorm.html

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