R. Jajte, “Pointwise ergodic theorem for unbounded operators in <nobr>$\mathbf{L}_2$</nobr>”, Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 4,Pages <nobr>806

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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.

Received: 28.09.2002
Revised: 15.05.2003

Language: English

DOI: 10.4213/tvp137