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Theorems · Theorem · functional analysis

ContinuousLinearMap.norm_inr_le_one

∀ (𝕜 : Type u_9) [inst : NontriviallyNormedField 𝕜] (E : Type u_10) (F : Type u_11) [inst_1 : SeminormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : SeminormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F],
  ‖ContinuousLinearMap.inr 𝕜 E F‖ ≤ 1
Defined in
Mathlib.Analysis.Normed.Operator.NormedSpace
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Foundations
Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpace
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Real · cited by 25697RealRingHom.id · cited by 18349RingHom.idNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldNorm.norm · cited by 5413Norm.normContinuousLinearMap · cited by 5352ContinuousLinearMapSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupContinuousLinearMap.inr · cited by 59ContinuousLinearMap.inrLinearIsometry.norm_toContinuousLinearMap_le · cited by 5LinearIsometry.norm_toCon…LinearIsometry.inr · cited by 3LinearIsometry.inrContinuousLinearMap.norm_inr_…CITED BYCITES

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