Riesz-Fischer theorem

Let {en} be an orthonormal basisMathworldPlanetmath for a (real or complex) infinite-dimensional Hilbert spaceMathworldPlanetmath . If {cn} is a sequence of (real or complex) numbers such that |cn|2 converges, then there is an x such that x=n=1cnen, and cn=x,en.

Title Riesz-Fischer theoremMathworldPlanetmath
Canonical name RieszFischerTheorem
Date of creation 2013-03-22 14:09:46
Last modified on 2013-03-22 14:09:46
Owner azdbacks4234 (14155)
Last modified by azdbacks4234 (14155)
Numerical id 7
Author azdbacks4234 (14155)
Entry type Theorem
Classification msc 46C99
Related topic LpSpace
Related topic L2SpacesAreHilbertSpaces
Related topic HilbertSpace
Related topic EllpXSpace
Related topic ClassificationOfHilbertSpaces