New York Journal of Mathematics
Volume 3A (1997-1998) 89-98


Roger L. Jones, Michael Lin, and James Olsen

Weighted Ergodic Theorems Along Subsequences of Density Zero

Published: March 18, 1998
Keywords: Besicovitch sequences, uniform sequences, Dunford-Schwartz operators, amplitude modulation, pointwise subsequence ergodic theorem
Subject: 47A35; 28A65

We consider subsequence versions of weighted ergodic theorems, and show that for a wide class of subsequences along which a.e. convergence of Cesaro averages has been established, we also have a.e. convergence for the subsequence Cesaro weighted averages, when the weights are obtained from uniform sequences produced by a connected apparatus.


R. Jones is partially supported by NSF Grant DMS--9531526

M. Lin is partially supported by the Israel Science Foundation

J. Olsen is partially supported by ND EPSCoR through NSF Grant # OSR-5452892

Author information

Roger L. Jones:
Department of Mathematics, DePaul University, 2219 N. Kenmore, Chicago, IL 60614

Michael Lin:
Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel

James Olsen:
Department of Mathematics, North Dakota State University, Fargo, N.D. 58105