Geodesic
On the weak convergence of operators iterations in von Neumann algebras
Vladikavkazskij matematičeskij žurnal, Tome 5 (2003) no. 3, pp. 39-45

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Equivalent conditions are obtained for the weak convergence of iterations of the positive contractions in the pre-conjugate spaces of von Neumann algebras. 
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     author = {A. A. Katz},
     title = {On the weak convergence of operators iterations in von {Neumann} algebras},
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A. A. Katz. On the weak convergence of operators iterations in von Neumann algebras. Vladikavkazskij matematičeskij žurnal, Tome 5 (2003) no. 3, pp. 39-45. http://geodesic.mathdoc.fr/item/VMJ_2003_5_3_a4/