International Journal of Mathematics and Mathematical Sciences

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

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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.