Theorems · Theorem · functional analysis
UnconditionalSchauderBasis.bddAbove_range_nnnorm_proj
∀ {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],
BddAbove (Set.range fun A => ‖GeneralSchauderBasis.proj b A‖₊)The projection norms are bounded above in a complete space.
- Defined in
- Mathlib.Analysis.Normed.Module.Bases
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement and proof · cited by 13,712
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normproof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- Set.rangestatement and proof · cited by 4,705
- NNRealstatement and proof · cited by 4,310
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalstatement · cited by 2,068
Cited by1
Results whose statement or proof uses this declaration.
- UnconditionalSchauderBasis.nnnorm_proj_le_nnnormProjBoundproof · cited by 1