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Theorems · Theorem · functional analysis

WeakDual.CharacterSpace.compContinuousMap_id

∀ (A : Type u_1) {𝕜 : Type u_4} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
  [inst_3 : CompleteSpace A] [inst_4 : StarRing A],
  WeakDual.CharacterSpace.compContinuousMap (StarAlgHom.id 𝕜 A) = ContinuousMap.id ↑(WeakDual.characterSpace 𝕜 A)

WeakDual.CharacterSpace.compContinuousMap sends the identity to the identity.

Defined in
Mathlib.Analysis.CStarAlgebra.GelfandDuality
Cited by
0 results in Mathlib
Foundations
Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedRingNormedAlgebraCompleteSpaceStarRing

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