On neveu decomposition and ergodic type theorems for semi-finite von Neumann algebras

Автор: Grabarnik Genady Ya., Katz Alexander A.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 2 т.5, 2003 года.

Бесплатный доступ

Some ergodic type theorems for automorphisms of semi-finite von Neumann algebras are considered. Neveu decomposition is employed in order to prove stochastical convergence. This work is a generalization of authors results from [5] to the case of semi-finite von Neumann algebras.

Короткий адрес: https://sciup.org/14318083

IDR: 14318083

Список литературы On neveu decomposition and ergodic type theorems for semi-finite von Neumann algebras

  • Akcoglu M., Sucheston L. A stochastic ergodic theorem for superadditive precesses//Ergodic Theory and Dynamical Systems.-1983.-V. 3.-P. 335-344.
  • Cunze J. P., Dang-Nqoc N. Ergodic theorems for noncommutative dynamical systems//Inventiones Mathematicae.-1978.-V. 46.-P. 1-15.
  • Goldstein M. S., Grabarnik G. Ya. Almost sure convergence theorems in von Neumann algebras//Israel J. Math.-1991.-V. 76.-P. 161-182.
  • Dixmier J. Les algebres d'operateurs dans l'espace hilbertien (algebres de von Neumann).-Paris: Gauthier-Villar, 1969.-367 p.
  • Grabarnik G. Ya., Katz A. A. Ergodic type theorems for finite von Neumann algebras//Israel J. Math.-1995.-V. 90.-P. 403-422.
  • Grabarnik G. Ya., Katz A. A. On multiparametric superadditive stochastic ergodic theorem for semi-finite von Neumann algebras/to appear.
  • Jajte R. Strong limit theorem in noncommutative probability//Lecture Notes in Math.-V. 1110.-Berlin: Spring-Verlag, 1985.-162 p.
  • Jajte R. On the existence of invariant states in W*-algebras//Bull. Polish Acad. Sci.-1986.-V. 34.-P. 617-624.
  • Hajian A., Kakutani S. Weakly wandering sets and invariant measures//Trans. Amer. Math. Soc.-1964.-V. 110.-P. 131-151.
  • Katz A. A. Ergodic type theorems in von Neumann algebras.-Ph. D. Thesis.-Pretoria: University of South Africa, 2001.-84 p.
  • Kingman J. F. C. Subadditive ergodic theory//Annals of Probability.-1973.-V. 1.-P. 883-909.
  • Kovacs I., Szucs J. Ergodic type theorem in von Neumann algebras//Acta Scientiarum Mathematicarum (Szeged).-1966.-V. 27.-P. 233-246.
  • Krengel U. Ergodic Theorems de Greuter.-Berlin, 1985.
  • Lance E. C. Ergodic theorems for convex sets and operator algebras//Inventiones Mathematicae.-1976.-V. 37.-P. 201-214.
  • Petz D. Ergodic theorems in von Neumann algebras//Acta Scientiarum Mathematicarum (Szeged).-1983.-V. 46.-P. 329-343.
  • Segal I. E. A noncommutative extension of abstract integration//Archiv der Math.-1953.-V. 57.-P. 401-457.
  • Синай Я. Г., Аншелевич В. В. Некоторые проблемы некоммутативной эргодической теории//Успехи мат. наук.-1976.-Т. 32.-С. 157-174.
  • Takesaki M. Theory of Operator Algebras. I.-Berlin: Springer-Verlag, 1979.-vii+415 p.
  • Yeadon F. J. Convergence of measurable operators//Math. Proc. Cambridge Philos. Soc.-1973.-V. 74.-P. 257-269.
  • Yeadon F. J. Ergodic theorems for semi-finite von Neumann algebras, I//J. London Math. Soc.-1977.-V. 16.-P. 326-332.
  • Yeadon F. J. Ergodic theorems for semi-finite von Neumann algebras, II//Math. Proc. Cambridge Philos. Soc.-1980.-V. 88.-P. 135-147.
Еще
Статья научная