On the ergodic Hilbert transform in L2 over a von Neumann algebra

• Autorzy: Kielanowicz K.
• Języki publikacji: EN

Abstrakty

EN

In this note a noncommutative version of Jajte’s theorem on the existence of the ergodic Hilbert transform is given. As a noncommutative counterpart of the classical almost everywhere convergence the bundle convergence of operators in a von Neumann algebra and its L₂-space is used.

Słowa kluczowe

EN

ergodic Hilbert transform; von Neumann algebra; bundle convergence

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2007
• Tom: Vol. 27, Fasc. 2
• Strony: 223--234
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Kielanowicz K.

• Faculty of Mathematics, University of Łódź, ul. Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [1] V. F. Gaposhkin, Criteria of the strong law of large numbers for some classes of stationary processes and homogeneous random fields, Theory Probab. Appl. 22 (1977), pp. 295-319.
• [2] Y. F. Gaposhkin, Individual ergodic theorem for normal operators in L2, Funct. Anal. Appl. 15 (1981), pp. 18-22.
• [3] E. Hensz and R. Jajte, Pointwise convergence theorems in L2 over a von Neumann algebra, Math. Z. 193 (1986), pp. 413-429.
• [4] E. Hensz, R. Jajte and A. Paszkiewicz, The bundle convergence in von Neumann algebras and their L2-spaces, Studia Math. 120 (1) (1996).
• [5] R. Jajte, On the existence of the ergodic Hilbert transform, Ann. Probab. 15 (1987), pp. 831-835.
• [6] R. Jajte, Strong Limit Theorems in Noncommutative L2-Spaces, Lecture Notes in Math. No 1477, Springer, Berlin-Heidelberg-New York 1991.