nonlinearRightInverseOfSurjective

English

In the situation of a surjective continuous linear map between Banach spaces, the constructed nonlinear right inverse has strictly positive NN-norm.

Русский

В ситуации сюръективного непрерывного линейного отображения между банаховыми пространствами построенное нелинейное правое обратное имеет строго положную NN-норму.

LaTeX

$$$0 < \\lVert g \\rVert_{NN}$ for the nonlinearRightInverseOfSurjective g$$

Lean4

/-- A surjective continuous linear map between Banach spaces admits a (possibly nonlinear)
controlled right inverse. In general, it is not possible to ensure that such a right inverse
is linear (take for instance the map from `E` to `E/F` where `F` is a closed subspace of `E`
without a closed complement. Then it doesn't have a continuous linear right inverse.) -/
noncomputable def nonlinearRightInverseOfSurjective :=
  val_proj @wrapped✝.{}

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