Riesz representation theorem RieszRepresentationTheorem 2004-02-16 07:11:51 2004-02-17 19:26:51 Theorem % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here 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 $u$.