View More View Less
  • 1 Hacettepe University, Ankara, Turkey, 06800
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

In this paper, we proved theorems which give the conditions that special operator nets on a predual of von Neumann algebras are strongly convergent under the Markov case. Moreover, we investigate asymptotic stability and existence of a lower-bound function for such nets.

  • [1]

    Akemann, C. A., The dual space of an operator algebra, Trans. Amer. Math. Soc., 126 (1967), 286302.

  • [2]

    Bartoszek, W., Erkursun, N., On quasi compact Markov nets, Ergodic Theory Dynam. Systems, 31(4) (2011), 1081094.

  • [3]

    Choi, M. D. and Effros, E. G., Injectivity and operator spaces, J. Funct. Anal., 24 (1977), 156209.

  • [4]

    Emel'yanov, E., Yu., Non-spectral asymptotic analysis of one-parameter operator semigroups, Operator Theory: Advance and Applications, 173, Birkháuser Verlag, Basel, 2007, viii+17 pp.

    • Search Google Scholar
    • Export Citation
  • [5]

    Emel'yanov, E. and Erkursun, N., Lotz-Rábiger's nets of Markov operators in L1-spaces, J. Math. Anal. Appl., 371(2) (2010), 777783.

    • Search Google Scholar
    • Export Citation
  • [6]

    Emel'yanov, E. and Erkursun, N., Generalization of Eberlein's and Sine's ergodic theorems to LR-nets, Vladikavkaz. Mat. Zh., 9(3) (2007), 2226.

    • Search Google Scholar
    • Export Citation
  • [7]

    Emel'yanov, E., Yu., Asymptotic Behavior of Lotz -Rábiger and Martingale Nets, Russian, with Russian summary, Sibirsk. Mat. Zh., 51(5) (2010), 10171026. (Translation in Siberian Math. J., 51(5) (2010), 810–817.)

    • Search Google Scholar
    • Export Citation
  • [8]

    Emel'yanov, E., Yu. and Wolff, M. P. H., Asymptotic behavior of Markov semigroups on preduals of von Neumann algebras, J. Math. Anal. Appl., 314 (2006), 749763.

    • Search Google Scholar
    • Export Citation
  • [9]

    Emel'yanov, E., Yu. and Wolff, M. P. H., Mean lower bounds for Markov operators, Ann. Polon. Math., 83 (2004), 1119.

  • [10]

    Krengel, U., Ergodic Theorems, De Gruyter, Berlin, New York (1985)

  • [11]

    Lasota, A., Statistical stability of deterministic systems, in: Equadiff 82,Wurzburg, 1982, in: Lecture Notes in Math., vol. 1017, Springer-Verlag, Berlin, 1983, 386419.

    • Search Google Scholar
    • Export Citation
  • [12]

    Lasota, A. and Mackey, M. C., Chaos, Fractals and Noise, Stochastic Aspects of Dynamics, second ed., Appl. Math. Sci.; Springer-Verlag, New York, 1993, Vol. 97, xiv+472.

    • Search Google Scholar
    • Export Citation
  • [13]

    Lotz, H. P., Tauberian theorems for operators on L1 and similar spaces, in: Biersted, K.-D., Fuchssteiner, B. (ed.) Functional Analysis: Surveys and Recent Results; Amsterdam: North Holland, 1984, 117133.

    • Search Google Scholar
    • Export Citation
  • [14]

    Rábiger, F., Stability and ergodicity of dominated semigroups. II. The strong case, Math. Ann., 297(1) (1993), 103116.

  • [15]

    Sakai, S., C*-algebras and W*-algebras; Ergeb. Math. Grenzgeb., Band 60, Springer-Verlag, New York, 1971.

  • [16]

    Sarymsakov, T. A. and Grabarnik, T. Ya., The regularity of monotone continuous compressions on von Neumann algebras; Dokl. AN Uz. SSR, 6 (1987), 911.

    • Search Google Scholar
    • Export Citation
  • [17]

    Takesaki, M., Theory of Operator Algebras I, Springer-Verlag, New York, 1979.

  • [18]

    Takesaki, M., Theory of Operator Algebras I, Springer-Verlag, New York, 1979.