Theorems · Theorem · functional analysis
ContinuousLinearMap.norm_snd
∀ (𝕜 : Type u_1) (E : Type u_2) (F : Type u_3) [inst : NontriviallyNormedField 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] [Nontrivial F], ‖ContinuousLinearMap.snd 𝕜 E F‖ = 1
The operator norm of the second projection E × F → F is exactly 1 if F is nontrivial.
- Defined in
- Mathlib.Analysis.Normed.Operator.Prod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Nontrivialstatement and proof · cited by 2,416
- le_antisymmproof · cited by 2,068
- norm_nonnegproof · cited by 725
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