norm_compContinuousLinearMapL_le — Mathlib

English

The operator norm of compContinuousLinearMapLRight is bounded by the norm of the generating multilinear map g.

Русский

Нормa оператора compContinuousLinearMapLRight ограничена нормой отображения g.

LaTeX

$$$ \|compContinuousLinearMapLRight (E := E) g\| ≤ \|g\| $$$

Lean4

theorem norm_compContinuousLinearMapL_le (f : ∀ i, E i →L[𝕜] E₁ i) :
    ‖compContinuousLinearMapL (G := G) f‖ ≤ ∏ i, ‖f i‖ :=
  LinearMap.mkContinuous_norm_le _ (by positivity) _

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