A Property of Weak Convergence of Positive Contractions of Von Neumann Algebras

In the present paper we prove that the mixing property of positive L1-contraction of finite von Neumann algebras implies the property of complete mixing.

Anahtar Kelimeler:

Positive contraction, mixing, completely mixing, von Neumann algebra

A Property of Weak Convergence of Positive Contractions of Von Neumann Algebras

In the present paper we prove that the mixing property of positive L1-contraction of finite von Neumann algebras implies the property of complete mixing.

Keywords:

Positive contraction, mixing, completely mixing, von Neumann algebra,

PDF

___

Akcoglu, M., Sucheston, L.: On operator convergence in Hilbert space and in Lebesgue space, Period. Math. Hungar. 2,235-244(1972).
Bratteli, O., Robinson, D.W.: Operator algebras and quantum statistical mechanics, I, New York Heidelberg Berlin:Springer 1979.
C¸ ¨omez, D., Litvinov, S.: Norm convergence of moving averages for τ -integrable operators, Rocky Mountain J. Math. 30, 1251-1263 (2000).
Dobrushin, R.L.: Central limit theorem for nonstationary Markov chains. I,II, Theor. Probab. Apll. 1,65-80; 329-383 (1956).
Fagnola, F., Rebolledo, R.: Transience and recurrence of quantum Markov semigroups. Probab. Theory Relat. Fields 126, 289-306 (2003).
Katz, A. A.: One property of the weak convergence of operators iterations in von Neumann algebras, Vladikavkaz Math. Jour. 5, 2 (2003), 34-35.
Krengel, U.: Ergodic Theorems, Walter de Gruyter, Berlin-New York 1985.
Litvinov, S. , Mukhamedov, F.: On individual subsequential ergodic theorem in von Neu- mann algebras, Studia Math. 145, 55-62(2001).
Luczak, A.: Qantum dynamical semigroups in strongly finite von Neumann algebras, Acta Math. Hungar. 92, 11-17 (2001).
Nelson, E.: Note on non-commutative integration, J. Funct. Anal. 15, 103-117 (1974).
Radjabalipour, M.: Additive mapping on von Neumann algebras preserving absolute values, Linear Algebra and its Appl. 368, 229-241 (2003).
Radjabalipour, M., Seddighi, K., Taghavi, Y.: Additive mapping on operator algebras preserving absolute values, Linear Algebra and its Appl. 327, 197-206 (2001).
Takesaki, M.: Theory of operator algebras, I, New York-Heidelberg- Berlin: Springer 1979. Farrukh MUKHAMEDOV
Department of Mechanics and Mathematics National University of Uzbekistan Vuzgorodok, 700174, Tashkent-UZBEKISTAN e-mail: far75m@yandex.ru Seyit TEM˙IR
Department of Mathematics, Arts and Science Faculty, Harran University, 63200, S¸anliurfa-TURKEY e-mail: seyittemir38@yahoo.com