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The Haar System in the Preduals of Hyperfinite Factors

Published online by Cambridge University Press:  20 November 2018

D. Potapov  and
F. Sukochev
D. Potapov
Affiliation:
School of Computer Science, Engineering and Mathematics, Flinders University, Bedford Park SA 5042, Australiae-mail: denis.potapov@flinders.edu.au
F. Sukochev
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Kensington NSW 2052, Australiae-mail: f.sukochev@unsw.edu.au
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Abstract

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

Keywords

46L52
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 2 , 01 June 2011 , pp. 347 - 363
Copyright
Copyright © Canadian Mathematical Society 2011

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