The definition of the predual given above seems to depend on the choice of Hilbert space that "M" acts on, as this determines the ultraweak topology. However the predual can also be defined without using the Hilbert space that "M" acts on, by defining it to be the space generated by all positive normal linear functionals on "M". (Here "normal" means that it preserves suprema when applied to increasing nets of self adjoint operators; or equivalently to increasing sequences of projections.)