infty_smulCommClass — Mathlib

English

The lp-infinite subring carries a ring structure and is closed under addition and multiplication.

Русский

Подкольцо lp ∞ обладает кольцевой структурой и замкнуто по сложению и умножению.

LaTeX

$$$lpInftySubring\\ B \\∞ : Subring (PreLp B)$ with carrier {f | Memℓp f ∞}$$

Lean4

instance infty_smulCommClass {𝕜} [NormedRing 𝕜] [∀ i, Module 𝕜 (B i)] [∀ i, IsBoundedSMul 𝕜 (B i)]
    [∀ i, SMulCommClass 𝕜 (B i) (B i)] : SMulCommClass 𝕜 (lp B ∞) (lp B ∞) :=
  ⟨fun r f g => lp.ext <| smul_comm (N := ∀ i, B i) (α := ∀ i, B i) r (⇑f) (⇑g)⟩

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