Theorems · Definition · functional analysis

InnerProductSpace.toDual

• 1000+ list: Riesz representation theorem

(𝕜 : Type u_1) →
  (E : Type u_2) →
    [inst : RCLike 𝕜] →
      [inst_1 : NormedAddCommGroup E] → [inst_2 : InnerProductSpace 𝕜 E] → [CompleteSpace E] → E ≃ₗᵢ⋆[𝕜] StrongDual 𝕜 E

Fréchet-Riesz representation: any ℓ in the dual of a Hilbert space E is of the form fun u => ⟪y, u⟫ for some y : E, i.e. toDualMap is surjective.

Defined in

Mathlib.Analysis.InnerProductSpace.Dual

Cited by

45 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpace