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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 4, Pages 806–818
DOI: https://doi.org/10.4213/tvp137 (Mi tvp137) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Pointwise ergodic theorem for unbounded operators in $\mathbf{L}_2$

R. Jajte

Institute of Mathematics, Warsaw University
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DOI: https://doi.org/10.4213/tvp137
Abstract: A condition implying the strong law of large numbers for trajectories of a normal unbounded operator is given. The condition has been described in terms of a spectral measure. To embrace the case of unbounded operators we pass from the classical arithmetic (Cesàro) means to the Borel methods of summability.
Keywords: strong law of large numbers, individual ergodic theorem, unbounded normal operator, spectral measure, Borel methods of summability, almost sure convergence.
Received: 28.09.2002
Revised: 15.05.2003
English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 4, Pages 662–676
DOI: https://doi.org/10.1137/S0040585X97982116
Bibliographic databases:
Document Type: Article
Language: English
Citation: R. Jajte, “Pointwise ergodic theorem for unbounded operators in $\mathbf{L}_2$”, Teor. Veroyatnost. i Primenen., 50:4 (2005), 806–818; Theory Probab. Appl., 50:4 (2006), 662–676
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v50/i4/p806
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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