toContinuousLinearMap — Mathlib

English

The restricted-scalar version satisfies the same operator-norm identity: ||smulRightL 𝕜 E Fₗ c f|| = ||c|| · ||f||.

Русский

Версия с ограничением скаляр вызывает ту же норму оператора: ||smulRightL 𝕜 E Fₗ c f|| = ||c|| · ||f||.

LaTeX

$$$ \\|smulRightL\\, 𝕜\\, E\\, F_\\ell\\, c\\, f\\| = \\|c\\| \\cdot \\|f\\| $$$

Lean4

/-- Construct a continuous linear map from `IsBoundedLinearMap`. -/
def toContinuousLinearMap {f : E → F} (hf : IsBoundedLinearMap 𝕜 f) : E →L[𝕜] F :=
  { toLinearMap f hf with
    cont :=
      let ⟨C, _, hC⟩ := hf.bound
      AddMonoidHomClass.continuous_of_bound (toLinearMap f hf) C hC }

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