International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 14, Pages 2307-2319

On weak convergence of iterates in quantum Lp-spaces (p1)

Genady Ya. Grabarnik,1 Alexander A. Katz,2 and Laura Shwartz3

1IBM T. J.Watson Research Center, 19 Skyline Drive, Hawthorne 10532, NY, USA
2Department of Mathematics and Computer Science, St. John's College of Liberal Arts and Sciences, St. John's University, 300 Howard Avenue, DaSilva Hall 314, Staten Island 10301, NY, USA
3Department of Mathematical Sciences, College of Science, Engineering and Technology, University of South Africa (UNISA), P.O. Box 392, Pretoria 0003, South Africa

Received 13 April 2005

Copyright © 2005 Genady Ya. Grabarnik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Equivalent conditions are obtained for weak convergence of iterates of positive contractions in the L1-spaces for general von Neumann algebra and general JBW algebras, as well as for Segal-Dixmier Lp-spaces (1p<) affiliated to semifinite von Neumann algebras and semifinite JBW algebras without direct summands of type I2.