Theorems · Definition · functional analysis

WithLp.unitization_addEquiv_prod

(𝕜 : Type u_1) →
  (A : Type u_2) →
    [inst : NormedField 𝕜] →
      [inst_1 : NonUnitalNormedRing A] → [NormedSpace 𝕜 A] → WithLp 1 (Unitization 𝕜 A) ≃+ WithLp 1 (𝕜 × A)

The natural map between Unitization 𝕜 A and 𝕜 × A, transferred to their WithLp 1 synonyms.

Defined in: Mathlib.Analysis.Normed.Algebra.UnitizationL1
Cited by: 1 results in Mathlib
Foundations: Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedField NonUnitalNormedRing NormedSpace

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

NormedSpacestatement and proof · cited by 12,499
ENNRealstatement · cited by 9,879
LinearEquiv.symmproof · cited by 1,461
AddEquivstatement · cited by 1,087
NormedFieldstatement and proof · cited by 1,084
WithLpstatement · cited by 345
NonUnitalNormedRingstatement and proof · cited by 231
Unitizationstatement and proof · cited by 220
LinearEquiv.toAddEquivproof · cited by 58
AddEquiv.transproof · cited by 53
WithLp.linearEquivproof · cited by 29
Unitization.addEquivproof · cited by 9

Cited by2

Results whose statement or proof uses this declaration.

WithLp.unitization_norm_defproof · cited by 2
WithLp.uniformEquiv_unitization_addEquiv_prodproof · cited by 0