Theorems · Definition · functional analysis

WithLp.unitizationAlgEquiv

{𝕜 : Type u_1} →
  {A : Type u_2} →
    [inst : NormedField 𝕜] →
      [inst_1 : NonUnitalNormedRing A] →
        [inst_2 : NormedSpace 𝕜 A] →
          [inst_3 : IsScalarTower 𝕜 A A] →
            [inst_4 : SMulCommClass 𝕜 A A] →
              (R : Type u_3) →
                [inst_5 : CommSemiring R] →
                  [inst_6 : Algebra R 𝕜] →
                    [inst_7 : DistribMulAction R A] →
                      [inst_8 : IsScalarTower R 𝕜 A] → WithLp 1 (Unitization 𝕜 A) ≃ₐ[R] Unitization 𝕜 A

equiv bundled as an algebra isomorphism with Unitization 𝕜 A.

Defined in

Mathlib.Analysis.Normed.Algebra.UnitizationL1

Cited by

4 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldNonUnitalNormedRingNormedSpaceIsScalarTowerSMulCommClassCommSemiringAlgebraDistribMulActionIsScalarTower