Theorems · Theorem · functional analysis
ContinuousLinearMap.opNorm_bound_of_ball_bound
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] {r : ℝ},
0 < r → ∀ (c : ℝ) (f : StrongDual 𝕜 E), (∀ z ∈ Metric.closedBall 0 r, ‖f z‖ ≤ c) → ‖f‖ ≤ c / r- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- RCLikestatement and proof · cited by 2,829
- LT.lt.leproof · cited by 2,189
- norm_nonnegproof · cited by 725
- Metric.closedBallstatement and proof · cited by 704
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.