Editing Riesz representation theorem (section)

{{Short description|Theorem about the dual of a Hilbert space}}
{{about|a theorem concerning the dual of a Hilbert space|the theorems relating linear functionals to measures|Riesz–Markov–Kakutani representation theorem|other theorems|Riesz theorem (disambiguation){{!}}Riesz theorem}}

The '''Riesz representation theorem''', sometimes called the '''Riesz–Fréchet representation theorem''' after [[Frigyes Riesz]] and [[Maurice René Fréchet]], establishes an important connection between a [[Hilbert space]] and its [[continuous dual space]]. If the underlying [[Field (mathematics)|field]] is the [[real number]]s, the two are [[isometry|isometrically]] [[isomorphism|isomorphic]]; if the underlying field is the [[complex number]]s, the two are isometrically [[anti-isomorphic]]. The (anti-) [[isomorphism]] is a particular [[natural isomorphism]].