tprodL_coe — Mathlib

English

The inverse of liftIsometry is given by composing with tprodL, matching the action on simple generators.

Русский

Обратное к liftIsometry задаётся композициями с tprodL, согласуясь с действием на простых порождающих.

LaTeX

$$liftIsometry_symm_apply (l) : (liftIsometry 𝕜 E F).symm l = l.compContinuousMultilinearMap (tprodL 𝕜)$$

Lean4

@[simp]
theorem tprodL_coe : (tprodL 𝕜).toMultilinearMap = tprod 𝕜 (s := E) :=
  by
  ext m
  simp only [ContinuousMultilinearMap.coe_coe, tprodL_toFun]

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