Theorems · Theorem · functional analysis
ContinuousAffineMap.norm_image_zero_le
∀ {𝕜 : Type u_1} {V : Type u_3} {W : Type u_4} [inst : SeminormedAddCommGroup V] [inst_1 : SeminormedAddCommGroup W]
[inst_2 : NontriviallyNormedField 𝕜] [inst_3 : NormedSpace 𝕜 V] [inst_4 : NormedSpace 𝕜 W] (f : V →ᴬ[𝕜] W),
‖f 0‖ ≤ ‖f‖- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ContinuousAffineMapstatement and proof · cited by 263
- le_max_leftproof · cited by 215
- ContinuousAffineMap.contLinearproof · cited by 45
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousAffineMap.norm_comp_leproof · cited by 0