Weierstrass functions separate all traces (Q2063666)

In this note, the authors generalize a result of [\textit{H.~Gimperlein} and \textit{M.~Goffeng}, Forum Math. Sigma 5, Paper No.~e3, 57~p. (2017; Zbl 1471.58007)] to the case of all traces on the weak \(L_1\)-ideal \(\mathscr{L}_{1,\infty}\). As a corollary, they show that the class of operators related to the quantum differentials of Weierstrass functions is large enough to separate all traces on the ideal \(\mathscr{L}_{1,\infty}\).