Theorems · Theorem · functional analysis

UnconditionalSchauderBasis.nnnorm_proj_le_nnnormProjBound

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {X : Type u_2} [inst_1 : NormedAddCommGroup X]
  [inst_2 : NormedSpace 𝕜 X] {β : Type u_3} (b : UnconditionalSchauderBasis β 𝕜 X) [CompleteSpace X] (A : Finset β),
  ‖GeneralSchauderBasis.proj b A‖₊ ≤ b.nnnormProjBound

The nnnorm of any projection is bounded by the basis constant.

Defined in

Mathlib.Analysis.Normed.Module.Bases

Cited by

1 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCompleteSpace