A Schauder basis for a Banach space 
is a sequence 
in 
with the property that every 
has a unique representation of the form 
for 
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]](/images/equations/SchauderBasis/Inline7.svg)
for 
.
Schauder Basis
See also
Banach SpaceThis 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.Referenced on Wolfram|Alpha
Schauder BasisCite this as:
Moslehian, Mohammad Sal. "Schauder Basis." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SchauderBasis.html