Theorems · Theorem · functional analysis

HilbertBasis.hasSum_repr_symm

∀ {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) (f : ↥(lp (fun x => 𝕜) 2)),
  HasSum (fun i => ↑f i • b i) (b.repr.symm f)

Defined in

Mathlib.Analysis.InnerProductSpace.l2Space

Cited by

1 results in Mathlib

Foundations

Depth 234 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace