International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 14, Pages 2307-2319
On weak convergence of iterates in quantum -spaces
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 -spaces for
general von Neumann algebra and general algebras, as well as
for Segal-Dixmier -spaces affiliated
to semifinite von Neumann algebras and semifinite algebras
without direct summands of type .