Weighted ergodic theorems for mean ergodic contractions
Authors:
Dogan Çömez, Michael Lin and James Olsen
Journal:
Trans. Amer. Math. Soc. 350 (1998), 101117
MSC (1991):
Primary 47A35, 28D99
MathSciNet review:
1433114
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Abstract: It is shown that any bounded weight sequence which is good for all probability preserving transformations (a universally good weight) is also a good weight for any contraction with mean ergodic (ME) modulus, and for any positive contraction of with . We extend the return times theorem by proving that if is a DunfordSchwartz operator (not necessarily positive) on a Lebesgue space, then for any bounded measurable is a universally good weight for a.e. We prove that if a bounded sequence has "Fourier coefficents", then its weighted averages for any contraction with mean ergodic modulus converge in norm. In order to produce weights, good for weighted ergodic theorems for contractions with quasiME modulus (i.e., so that the modulus has a positive fixed point supported on its conservative part), we show that the modulus of the tensor product of contractions is the product of their moduli, and that the tensor product of positive quasiME contractions is quasiME.
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 A. Bellow and V. Losert, The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences, Trans. AMS, 288 (1985), 307345. MR 86c:28035
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 Y. Ito, Uniform integrability and the pointwise ergodic theorem, Proc. AMS, 16 (1965), 222227. MR 30:2121
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Additional Information
Dogan Çömez
Affiliation:
Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105
Michael Lin
Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva, Israel
James Olsen
Affiliation:
Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105
DOI:
http://dx.doi.org/10.1090/S0002994798019862
PII:
S 00029947(98)019862
Received by editor(s):
October 9, 1995
Dedicated:
Dedicated to the Memory of Professor Robert Sine
Article copyright:
© Copyright 1998 American Mathematical Society
