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Contents of PMS, Vol. 23, Fasc. 1,
pages 173 - 187
 

MULTIPARAMETER SUPERADDITIVE ERGODIC THEOREMS FOR MEAN ERGODIC L1 -CONTRACTIONS

Doğan Cömez
Michael Lin

Abstract: Let T and S be commuting Markovian operators on L (X). 1 We prove that when the operators are mean ergodic and (F ) (m,n) is a directionally (T,S) -superadditive dominated process, then the “averages” n-2F (n,n) converge in L 1 -norm. If, further, the process is strongly superadditive, then the same averages converge a.e. as well.

1991 AMS Mathematics Subject Classification: 47A3S, 28D99.

Key words and phrases: Superadditive processes, Markovian operators, mean ergodic L1 -contractions.

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