Theorems · Theorem · functional analysis

OrthogonalFamily.orthonormal_sigma_orthonormal

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {ι : Type u_4} {G : ι → Type u_5} [inst_3 : (i : ι) → NormedAddCommGroup (G i)]
  [inst_4 : (i : ι) → InnerProductSpace 𝕜 (G i)] {V : (i : ι) → G i →ₗᵢ[𝕜] E},
  OrthogonalFamily 𝕜 G V →
    ∀ {α : ι → Type u_6} {v_family : (i : ι) → α i → G i},
      (∀ (i : ι), Orthonormal 𝕜 (v_family i)) → Orthonormal 𝕜 fun a => (V a.fst) (v_family a.fst a.snd)

Defined in

Mathlib.Analysis.InnerProductSpace.Subspace

Cited by

1 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpace