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# The Haar System in the Preduals of Hyperfinite Factors

Published:2011-01-26
Printed: Jun 2011
• D. Potapov,
School of Computer Science, Engineering and Mathematics, Flinders University, Bedford Park SA 5042, AUSTRALIA
• F. Sukochev,
School of Mathematics and Statistics, University of New South Wales, Kensington NSW 2052, AUSTRALIA
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## Abstract

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).
 MSC Classifications: 46L52 - Noncommutative function spaces