opNNNorm_prod — Mathlib

English

The operator norm is subadditive: ∥f + g∥ ≤ ∥f∥ + ∥g∥.

Русский

Норма оператора подаддитивна: ∥f + g∥ ≤ ∥f∥ + ∥g∥.

LaTeX

$$$$ \\|f + g\\| ≤ \\|f\\| + \\|g\\|.$$$$

Lean4

theorem opNNNorm_prod (f : ContinuousMultilinearMap 𝕜 E G) (g : ContinuousMultilinearMap 𝕜 E G') :
    ‖f.prod g‖₊ = max ‖f‖₊ ‖g‖₊ :=
  eq_of_forall_ge_iff fun _ ↦ by simp only [opNNNorm_le_iff, prod_apply, Prod.nnnorm_def, max_le_iff, forall_and]

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