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Schauder Basis


A Schauder basis for a Banach space X is a sequence {x_n} in X with the property that every x in X has a unique representation of the form x=sum_(n=1)^(infty)alpha_nx_n for alpha_n in C in which the sum is convergent in the norm topology. For example, the trigonometrical system is a basis in each space L^p[0,1] for 1<p<infty.


See also

Banach Space

This entry contributed by Mohammad Sal Moslehian

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References

Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. Experimental Mathematics in Action. Wellesley, MA: A K Peters, pp. 115-117, 2007.Johnson, W. B. and Lindenstrauss, J. (Eds.). Handbook of the Geometry of Banach Spaces, Vol. 1. Amsterdam, Netherlands: North-Holland, 2001.

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Schauder Basis

Cite this as:

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

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