Theorems · Definition · functional analysis

HilbertBasis.repr

{ι : Type u_1} →
  {𝕜 : Type u_2} →
    [inst : RCLike 𝕜] →
      {E : Type u_3} →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : InnerProductSpace 𝕜 E] → HilbertBasis ι 𝕜 E → E ≃ₗᵢ[𝕜] ↥(lp (fun x => 𝕜) 2)

The linear isometric equivalence implementing identifying the Hilbert space with ℓ².

Defined in

Mathlib.Analysis.InnerProductSpace.l2Space

Cited by

12 results in Mathlib

Foundations

Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace