norm_mkPiAlgebraFin_le — Mathlib

English

The operator norm of the SmulRight action by z satisfies the equality with the product of the operator norm of f and the norm of z. This is the real-valued counterpart to the NN-norm relation.

Русский

Норма оператора действия SmulRight на z равна произведению нормы f на норму z.

LaTeX

$$$\|f\!\cdot\! z\| = \|f\| \cdot \|z\|$$$

Lean4

theorem norm_mkPiAlgebraFin_le : ‖ContinuousMultilinearMap.mkPiAlgebraFin 𝕜 n A‖ ≤ max 1 ‖(1 : A)‖ :=
  by
  cases n
  · exact norm_mkPiAlgebraFin_zero.le.trans (le_max_right _ _)
  · exact (norm_mkPiAlgebraFin_le_of_pos (Nat.zero_lt_succ _)).trans (le_max_left _ _)

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