Theorems · Theorem · functional analysis
ContinuousLinearMap.norm_single_le_one
∀ {ι : Type u_9} [inst : Fintype ι] [inst_1 : DecidableEq ι] (𝕜 : Type u_10) [inst_2 : NontriviallyNormedField 𝕜]
(E : ι → Type u_11) [inst_3 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_4 : (i : ι) → NormedSpace 𝕜 (E i)]
(i : ι), ‖ContinuousLinearMap.single 𝕜 E i‖ ≤ 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ContinuousLinearMap.singlestatement · cited by 14
- LinearIsometry.norm_toContinuousLinearMap_leproof · cited by 5
- LinearIsometry.singleproof · cited by 2
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