One property of the weak covergence of operators iterations in von Neumann algebras
Vladikavkazskij matematičeskij žurnal, Tome 5 (2003) no. 2, pp. 34-35
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Conditions are given for *-weak convergence of iterations for an ultraweak continuous fuctional in von Neumann algebra to imply norm convergence.
[1] Bratteli O., Robinson D., Operator Algebras and Quantum Statistical Mechanics, Springer-Verlag, New York–Heidelberg–Berlin, 1979, 500 pp. | MR | Zbl
[2] Katz A. A., Ergodic Type Theorem in von Neumann Algebras, Ph. D. Thesis, University of South Africa, Pretoria, 2001, 84 pp.
[3] Pedersen G. K., $C^*$-algebras and their automorphism groups, Academic Press, London–New York–San Fransisco, 1979, 416 pp. | MR | Zbl
[4] Sakai S., $C^*$-algebras and $W^*$-algebras, Springer-Verlag, Berlin, 1971, 256 pp. | MR | Zbl
[5] Takesaki M., Theory of Operator Algebras, v. I, Springer-Verlag, Berlin, 1979, vii+415 pp. | MR