Theorems · Theorem · functional analysis

NormedSpace.toLinearMap_inclusionInDoubleDualWeak

∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] (X : Type u_2) [inst_1 : SeminormedAddCommGroup X]
  [inst_2 : NormedSpace 𝕜 X],
  ↑(NormedSpace.inclusionInDoubleDualWeak 𝕜 X) =
    ((toWeakSpace 𝕜 X).arrowCongr StrongDual.toWeakDual) ↑(NormedSpace.inclusionInDoubleDual 𝕜 X)

Defined in: Mathlib.Analysis.Normed.Module.DoubleDual
Cited by: 0 results in Mathlib
Foundations: Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField SeminormedAddCommGroup NormedSpace

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DFunLike.coestatement · cited by 62,936
RingHom.idstatement · cited by 18,349
NormedSpacestatement and proof · cited by 12,499
LinearMapstatement · cited by 10,215
NontriviallyNormedFieldstatement and proof · cited by 8,742
LinearEquivstatement · cited by 3,317
SeminormedAddCommGroupstatement and proof · cited by 2,671
ContinuousLinearMap.toLinearMapstatement · cited by 528
StrongDualstatement · cited by 459
WeakDualstatement · cited by 103
LinearEquiv.arrowCongrstatement · cited by 28
StrongDual.toWeakDualstatement · cited by 19

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