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