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
Statement Form Statement Form Connections
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
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.