instUnitizationNormedAddCommGroup

English

The uniform version of the above is an UniformEquiv between WithLp 1 (Unitization 𝕜 A) and WithLp 1 (𝕜 × A).

Русский

УнитизацияUniformEx: UniformEquiv между WithLp 1 (Unitization 𝕜 A) и WithLp 1 (𝕜 × A).

LaTeX

$$$$\\text{uniformEquiv\_unitization\_addEquiv\_prod} : WithLp 1 (Unitization 𝕜 A) \\simeq_u WithLp 1 (𝕜 \\times A).$$$$

Lean4

noncomputable instance instUnitizationNormedAddCommGroup : NormedAddCommGroup (WithLp 1 (Unitization 𝕜 A)) :=
  NormedAddCommGroup.induced (WithLp 1 (Unitization 𝕜 A)) (WithLp 1 (𝕜 × A)) (unitization_addEquiv_prod 𝕜 A)
    (AddEquiv.injective _)

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