# Riesz representation theorem

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

Title Riesz representation theorem RieszRepresentationTheorem 2013-03-22 14:09:43 2013-03-22 14:09:43 azdbacks4234 (14155) azdbacks4234 (14155) 9 azdbacks4234 (14155) Theorem msc 46C99 RieszFischerTheorem