Theorems · Theorem · functional analysis

SchauderBasis.proj_comp

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {X : Type u_2} [inst_1 : NormedAddCommGroup X]
  [inst_2 : NormedSpace 𝕜 X] (b : SchauderBasis 𝕜 X) (n m : ℕ) (x : X), (b.proj n) ((b.proj m) x) = (b.proj (min n m)) x

Composition of projections: proj n (proj m x) = proj (min n m) x.

Defined in

Mathlib.Analysis.Normed.Module.Bases

Cited by

0 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace