Riesz representation theorem

For every continuous linear functional $f$ on a Hilbert space $\mathscr{H}$, there is a unique $u\in \mathscr{H}$ such that $f(x)=⟨x,u⟩$ for all $x\in \mathscr{H}$.
Note: $⟨x,u⟩$ denotes the inner product between $x$ and $u$.

Title	Riesz representation theorem
Canonical name	RieszRepresentationTheorem
Date of creation	2013-03-22 14:09:43
Last modified on	2013-03-22 14:09:43
Owner	azdbacks4234 (14155)
Last modified by	azdbacks4234 (14155)
Numerical id	9
Author	azdbacks4234 (14155)
Entry type	Theorem
Classification	msc 46C99
Related topic	RieszFischerTheorem