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Contents of PMS, Vol. 22, Fasc. 1,
pages 85 - 99
 

INDIVIDUAL ERGODIC THEOREM FOR NON-CONTRACTIVE NORMAL OPERATORS

Ryszard Jajte

Abstract: A condition implying the strong law of large numbers for trajectories of a normal non-contractive operator is given. The condition has been described in terms of a spectral measure, in the spirit of the well-known theorem of V. F. Gaposhkin. To embrace the non-contractive operators we pass from the classical arithmetic (Cesŕro) means to the Borel methods of summability.

1991 AMS Mathematics Subject Classification: 47A3S, 60F1S.

Key words and phrases: Strong law of large numbers, individual ergodic theorem, normal operator, spectral measure, (non-)contractivity, Borel methods of summability, Mittag-Leffler’s function, almost sure convergence.

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