Abstract
We study systems of eigenspaces arising from the representation of a Vilenkin group on a semifinite von Neumann algebra. In particular, such systems form a Schauder decomposition in the reflexive non-communative $L_p$-spaces of measurable operators affiliated with the underlying von Neumann algebra. Our results extend classical results of Paley concerning the familiar Walsh-Paley system to the non-commutative setting.
Information
Published: 1 January 2001
First available in Project Euclid: 17 November 2014
zbMATH: 1124.46306
MathSciNet: MR1852692
Rights: Copyright © 2001, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.
