Surely you can define such notation, but why? The following is just as clear and concise, and does not rely on any extensions:

    (. * 2) <$> [1,2,3]

For example:

    def byTwo (inputList : List Nat) :=
      (. * 2) <$> inputList

    #eval byTwo [1, 2, 3]
    -- [2, 4, 6]