Theorems · Theorem · functional analysis

Submodule.isHilbertSumOrthogonal

∀ {𝕜 : Type u_2} [inst : RCLike 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  [inst_3 : CompleteSpace E] (K : Submodule 𝕜 E) [hK : CompleteSpace ↥K],
  IsHilbertSum 𝕜 (fun b => ↥(bif b then K else Kᗮ)) fun b => (bif b then K else Kᗮ).subtypeₗᵢ

Defined in

Mathlib.Analysis.InnerProductSpace.l2Space

Cited by

0 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpaceCompleteSpace