def METHOD_NAME(
    hilbert: _AbstractHilbert, site: int, dtype: _DType = float
) -> _LocalOperator:
    """
    Builds the :math:`\\sigma^{+} = \\frac{1}{2}(\\sigma^x + i \\sigma^y)` operator acting on the
    `site`-th of the Hilbert space `hilbert`.
    If `hilbert` is a non-Spin space of local dimension M, it is considered
    as a (M-1)/2 - spin space.
    :param hilbert: The hilbert space
    :param site: the site on which this operator acts
    :return: a nk.operator.LocalOperator
    """
    import numpy as np
    N = hilbert.size_at_index(site)
    S = (N - 1) / 2
    S2 = (S + 1) * S
    D = np.array([np.sqrt(S2 - m * (m + 1)) for m in np.arange(S - 1, -(S + 1), -1)])
    mat = np.diag(D, 1)
    mat = _sparse.coo_matrix(mat)
    return _LocalOperator(hilbert, mat, [site], dtype=dtype)