Theorems · Theorem · functional analysis

HilbertBasis.hasSum_inner_mul_inner

∀ {ι : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] (b : HilbertBasis ι 𝕜 E) (x y : E),
  HasSum (fun i => inner 𝕜 x (b i) * inner 𝕜 (b i) y) (inner 𝕜 x y)

Defined in

Mathlib.Analysis.InnerProductSpace.l2Space

Cited by

3 results in Mathlib

Foundations

Depth 236 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace