continuousMultilinearMapCongrRight_apply

English

The operator norm of the composed multilinear map is bounded by the product of norms of the composing linear maps.

Русский

Норма оператора композиции много-линейных отображений ограничена произведением норм линейных отображений, составляющих композицию.

LaTeX

$$$ \|g.compContinuousLinearMap f\| ≤ \|g\| \cdot \prod_i \|f_i\| $$$

Lean4

@[simp]
theorem _root_.ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply (g : G ≃L[𝕜] G')
    (f : ContinuousMultilinearMap 𝕜 E G) :
    g.continuousMultilinearMapCongrRight E f = (g : G →L[𝕜] G').compContinuousMultilinearMap f :=
  rfl

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