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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 4, Pages 806–818 (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

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.

DOI: https://doi.org/10.4213/tvp137

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English version:
Theory of Probability and its Applications, 2006, 50:4, 662–676

Bibliographic databases:

Received: 28.09.2002
Revised: 15.05.2003
Language:

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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\paper Pointwise ergodic theorem for unbounded operators in~$\mathbf{L}_2$
\jour Teor. Veroyatnost. i Primenen.
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\elib{http://elibrary.ru/item.asp?id=9157520}
\transl
\jour Theory Probab. Appl.
\yr 2006
\vol 50
\issue 4
\pages 662--676
\crossref{https://doi.org/10.1137/S0040585X97982116}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000243284300008}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Jajte R., “Pointwise limit theorem for a class of unbounded operators in $\mathbb L^r$-spaces”, Studia Math., 179:1 (2007), 49–61  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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