On weak convergence of iterates in quantum L_p-spaces (p ≥ 1)

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 (1 ≤ p < ∞) affiliated to semifinite von Neumann algebras and semifinite JBW algebras without direct summands of type I2. Copyright © 2005 Hindawi Publishing Corporation.