Theorems · Theorem · functional analysis

SchauderBasis.exists_norm_proj_le

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {X : Type u_2} [inst_1 : NormedAddCommGroup X]
  [inst_2 : NormedSpace 𝕜 X] (b : SchauderBasis 𝕜 X) [CompleteSpace X], ∃ C, ∀ (n : ℕ), ‖b.proj n‖ ≤ C

The projections are uniformly bounded.

Defined in

Mathlib.Analysis.Normed.Module.Bases

Cited by

1 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCompleteSpace