 In the special case where \(\Omega = \Omega(\mathbf{H})\), the set of density operators on a Hilbert space \(\mathbf{H}\), one can show that every effect \(f\) on \(\Omega\) has the form \(\,f(W) = \textrm{Tr}(W a)\) for a unique positive self-adjoint operator \(a\) with \(a \leq 1\). Conversely, such an operator defines an effect through the formula just given. One therefore identifies \(\mathcal{E}(\Omega(\mathbf{H}))\) with the set \(\mathcal{E}(\mathbf{H})\) of all positive self-adjoint operators on \(\mathbf{H})\) with \(0 \leq a \leq 1\), referring to these also as effects.