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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def proximal_linfty(space):
 r"""Proximal operator factory of the ``l_\infty``-norm. Function for the proximal operator of the functional ``F`` where ``F`` is the ``l_\infty``-norm:: ``F(x) = \sup_i |x_i|`` Parameters space : `LinearSpace` Domain of ``F``. Returns ------- prox_factory : callable Factory for the proximal operator to be initialized. Notes ----- The proximal is computed by the Moreau identity and a projection onto an l1-ball [PB2014]. See Also -------- proj_l1 : projection onto l1-ball """

    class ProximalLInfty(Operator):

        """Proximal operator of the linf-norm."""

        def __init__(self, sigma):
            """Initialize a new instance.

            Parameters
            ----------
            sigma : positive float
                Step size parameter
            """
            super(ProximalLInfty, self).__init__(
                domain=space, range=space, linear=False)
            self.sigma = float(sigma)

        def _call(self, x, out):
            """Return ``self(x)``."""

            radius = 1

            if x is out:
                x = x.copy()

            proj_l1(x, radius, out)
            out.lincomb(-1, out, 1, x)

    return ProximalLInfty