toContinuousLinearMap — Mathlib

English

The underlying MultilinearMap of 0 is 0: (0).toMultilinearMap = 0.

Русский

Базовая мультиляйная карта нуля равна нулю: (0).toMultilinearMap = 0.

LaTeX

$$$ (0 : \\mathrm{ContinuousMultilinearMap})^{\\text{toMultilinearMap}} = 0 $$$

Lean4

/-- If `f` is a continuous multilinear map, then `f.toContinuousLinearMap m i` is the continuous
linear map obtained by fixing all coordinates but `i` equal to those of `m`, and varying the
`i`-th coordinate. -/
@[simps!]
def toContinuousLinearMap [DecidableEq ι] (m : ∀ i, M₁ i) (i : ι) : M₁ i →L[R] M₂ :=
  { f.toMultilinearMap.toLinearMap m i with cont := f.cont.comp (continuous_const.update i continuous_id) }

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