le_opNNNorm — Mathlib

English

For a family f : ι' → ContinuousAlternatingMap, the norm of their product pi f equals the norm of f.

Русский

Для семейства f: ι' → ContinuousAlternatingMap, норма их произведения pi f равна норме f.

LaTeX

$$$$\|\pi f\| = \|f\|.$$$$

Lean4

/-- The fundamental property of the operator norm of a continuous alternating map:
`‖f m‖` is bounded by `‖f‖` times the product of the `‖m i‖`, `nnnorm` version. -/
theorem le_opNNNorm (f : E [⋀^ι]→L[𝕜] F) (m : ι → E) : ‖f m‖₊ ≤ ‖f‖₊ * ∏ i, ‖m i‖₊ :=
  f.1.le_opNNNorm m

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