Theorems · Definition · functional analysis

LinearIsometryEquiv.withLpProdComm

(p : ENNReal) →
  (𝕜 : Type u_1) →
    (α : Type u_2) →
      (β : Type u_3) →
        [hp : Fact (1 ≤ p)] →
          [inst : Semiring 𝕜] →
            [inst_1 : SeminormedAddCommGroup α] →
              [inst_2 : Module 𝕜 α] →
                [inst_3 : SeminormedAddCommGroup β] → [inst_4 : Module 𝕜 β] → WithLp p (α × β) ≃ₗᵢ[𝕜] WithLp p (β × α)

Commutativity of the L^p product as a linear isometric equivalence.

Defined in

Mathlib.Analysis.Normed.Lp.ProdLp

Cited by

2 results in Mathlib

Foundations

Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactSemiringSeminormedAddCommGroupModuleSeminormedAddCommGroupModule