norm_compContinuousLinearMap_le — Mathlib

English

If an alternating map f is bounded by C on all arguments, its mkContinuous version has norm at most C.

Русский

Если отображение f ограничено по норме на всех аргументах величиной C, его mkContinuous имеет норму не более C.

LaTeX

$$$\|f.mkContinuous C H\| \le C$$$

Lean4

theorem norm_compContinuousLinearMap_le (f : F [⋀^ι]→L[𝕜] G) (g : E →L[𝕜] F) :
    ‖f.compContinuousLinearMap g‖ ≤ ‖f‖ * (‖g‖ ^ Fintype.card ι) :=
  (f.1.norm_compContinuousLinearMap_le _).trans_eq <| by simp

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