continuousMultilinearMapCongrLeft_apply

English

The operator norm of the composed continuous multilinear map in the presence of a symmetric equivalence matches the product of the operator norms.

Русский

Нормa композиции непрерывного много-линейного отображения соответствует произведению норм оператора.

LaTeX

$$$ \|g.compContinuousMultilinearMap f\| ≤ \|g\| \cdot \|f\| $$$

Lean4

@[simp]
theorem _root_.ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply (g : ContinuousMultilinearMap 𝕜 E₁ G)
    (f : ∀ i, E i ≃L[𝕜] E₁ i) :
    ContinuousLinearEquiv.continuousMultilinearMapCongrLeft G f g =
      g.compContinuousLinearMap fun i => (f i : E i →L[𝕜] E₁ i) :=
  rfl

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