  We shall present examples of Schauder bases in the preduals to the
hyperfinite factors of types $\hbox{II}_1$, $\hbox{II}_\infty$,
$\hbox{III}_\lambda$, $0 < \lambda \leq 1$. In the semifinite (respectively,
purely infinite) setting, these systems form Schauder bases in any associated
separable symmetric space of measurable operators (respectively, in any
non-commutative $L^p$-space).
