Theorems · Theorem · functional analysis
ContinuousAffineMap.norm_eq
∀ {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 = 0 → ‖f‖ = ‖f.contLinear‖- Cited by
- 0 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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 and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- norm_nonnegproof · cited by 725
- norm_zeroproof · cited by 366
- ContinuousAffineMapstatement and proof · cited by 263
- max_eq_rightproof · cited by 79
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