Theorems · Theorem · functional analysis

GeneralSchauderBasis.proj_apply_basis_mem

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {X : Type u_2} [inst_1 : NormedAddCommGroup X]
  [inst_2 : NormedSpace 𝕜 X] {β : Type u_3} {L : SummationFilter β} (b : GeneralSchauderBasis β 𝕜 X L) (A : Finset β)
  (i : β), (b.proj A) (↑b i) = if i ∈ A then ↑b i else 0

The action of the projection on a basis element e i.

Defined in

Mathlib.Analysis.Normed.Module.Bases

Cited by

2 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace