Theorems · Theorem · functional analysis

OrthogonalFamily.summable_of_lp

∀ {ι : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] {G : ι → Type u_4} [inst_3 : (i : ι) → NormedAddCommGroup (G i)]
  [inst_4 : (i : ι) → InnerProductSpace 𝕜 (G i)] [CompleteSpace E] {V : (i : ι) → G i →ₗᵢ[𝕜] E},
  OrthogonalFamily 𝕜 G V → ∀ (f : ↥(lp G 2)), Summable fun i => (V i) (↑f i)

Defined in

Mathlib.Analysis.InnerProductSpace.l2Space

Cited by

1 results in Mathlib

Foundations

Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceCompleteSpace