Theorems · Definition · functional analysis

HilbertBasis.toUnconditionalSchauderBasis

{ι : Type u_1} →
  {𝕜 : Type u_2} →
    [inst : RCLike 𝕜] →
      {E : Type u_3} →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : InnerProductSpace 𝕜 E] → HilbertBasis ι 𝕜 E → UnconditionalSchauderBasis ι 𝕜 E

A Hilbert basis of is an unconditional Schauder basis (UnconditionalSchauderBasis), with coordinate functionals x ↦ ⟪b i, x⟫. The basis expansion x = ∑' i, ⟪b i, x⟫ • b i converges unconditionally.

Defined in

Mathlib.Analysis.InnerProductSpace.l2Space

Cited by

2 results in Mathlib

Foundations

Depth 237 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace