instUnitizationNormedAlgebra — Mathlib

English

There is a canonical algebra over ENNReal on WithLp 1 (Unitization 𝕜 A) compatible with the scalar tower structure.

Русский

Существует каноническая алгебра над ENNReal на WithLp 1 (Unitization 𝕜 A), совместимая с торовой структурой скаляров.

LaTeX

$$$\text{Algebra ENNReal}(WithLp 1 (Unitization 𝕜 A))$$$

Lean4

noncomputable instance instUnitizationNormedAlgebra : NormedAlgebra 𝕜 (WithLp 1 (Unitization 𝕜 A)) where
  norm_smul_le r
    x := by
    simp_rw [unitization_norm_def, ofLp_smul, fst_smul, snd_smul, norm_smul, mul_add]
    exact le_rfl

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