Every bounded linear functional on a Hilbert space can be represented uniquely as an inner product with a fixed vector of that space. Named for Frigyes Riesz, related versions represent functionals on spaces of continuous functions by measures.
Facts
StatementEvery continuous linear functional on a Hilbert space can be represented uniquely as the inner product with some fixed vector in that space. 1 Proof YearAttributed jointly to Riesz and Fréchet. Classification
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Source Riesz Representation Theorem (Wikipedia)
Sources
1. Riesz Representation Theorem (Wikipedia)
Wikimedia FoundationLead section, opening definition
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.
Lead section, sentence dating the theorem to 1907
Historically, the theorem is often attributed simultaneously to Riesz and Fréchet in 1907
Proved By: Frigyes Riesz, Lead
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.
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