The Haar system in the preduals of hyperfinite factors

Abstract

We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types ${II}_1$, ${II}_{\infty }$, ${III}_{\lambda }$, $0<\lambda \le 1$. 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).

18 pages