Theorems · Theorem · functional analysis

SchauderBasis.RankOneDecomposition.exists_coeff

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {X : Type u_2} [inst_1 : NormedAddCommGroup X]
  [inst_2 : NormedSpace 𝕜 X] (D : SchauderBasis.RankOneDecomposition 𝕜 X) (n : ℕ) (x : X),
  ∃ c, c • D.e n = (SchauderBasis.succSub D.P n) x

There exists a coefficient scaling e n to match (succSub D.P n) x.

Defined in

Mathlib.Analysis.Normed.Module.Bases

Cited by

1 results in Mathlib

Foundations

Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace