On the unconditional bundle convergence in L(2)-space over a von Neumann algebra

• Autorzy: Skalski A.
• Języki publikacji: EN

Abstrakty

EN

The Tandori theorem concerning the sufficient condition for the unconditional a.e. convergence of orthogonal series is generalized for the bundle convergencein L₂-space over a σ-finite von Neumann algebra. The result implies a noncommutative version of the Orlicz theorem proved earlier by Hensz, Jajte and Paszkiewicz.

Słowa kluczowe

EN

Neumann algebra; Orlicz theorem; Tandori theorem

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 1
• Strony: 19--27
• Opis fizyczny: Biblogr. 10 poz.

Twórcy

autor

Skalski A.

• Department of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Bibliografia

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• [2] E. Hensz and R. Jajte, Pointwise convergence theorems in L2 over a von Neumann algebra, Math. Z. 193 (1986), pp. 413-429.
• [3] E. Hensz, R. Jajte and A. Paszkiewicz, The unconditional pointwise convergence in L2 over a von Neumann algebra, Colloq. Math. 69 (1995), pp. 167-178.
• [4] E. Hensz, R. Jajte and A. Paszkiewicz, The bundle convergence in von Neumann algebras and their L2 spaces, Studia Math. 120 (1996), pp. 23-46.
• [5] R. Jajte, Strong limit theorems in noncommutative L2 spaces, Lecture Notes in Math. 1477, Springer, Berlin-Heidelberg-New York 1991.
• [6] E. C. Lance, Ergodic theorem for convex sets and operator algebras, Invent Math. 37 (1976), pp. 201-214.
• [7] B. Le Gac and F. Móricz, On the bundle convergence of orthogonal series and SLLN in noncommutative L2 spaces, Acta Sei. Math. (Szeged) 64 (1998), pp. 575-599.
• [8] W. Or licz, Zur Theorie der orthogonalen Reihen, Bull. Internat. Acad. Polon. Sci. Sér. A (1927), pp. 81-115.
• [9] D. Petz, Quasi-uniform ergodic theorems in von Neumann algebra, Bull. London Math. Soc. 16 (1984), pp. 151-156.
• [10] K. Tandori, Über die orthogonalen Funktionen X (unbedingte Konvergenz), Acta Sei. Math. (Szeged) 23 (1962), pp. 185-221.