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Banach Limit

A Banach limit is a bounded linear functional f on the space ł^infty of complex bounded sequences that satisfies ||f||=f(1)=1 and f({a_(n+1)})=f({a_n}) for all {a_n} in ł^infty.

This entry contributed by Mohammad Sal Moslehian

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References

Conway, J. A Course in Functional Analysis. New York: Springer-Verlag, 1990.Feldman, M. and Gilles, C. "An Expository Note on Individual Risk Without Aggregate Uncertainty." J. Econ. Theory 35, 26-32, 1985.

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Banach Limit

Cite this as:

Moslehian, Mohammad Sal. "Banach Limit." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/BanachLimit.html

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