On the individual ergodic theorem for positive operators
Author:
Ryōtarō Satō
Journal:
Proc. Amer. Math. Soc. 36 (1972), 456458
MSC:
Primary 47A35; Secondary 28A65
MathSciNet review:
0308820
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Abstract 
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Abstract: A theorem which gives a condition on a positive linear contraction on an space in order that the individual ergodic theorem hold is proved. The theorem contains a result obtained by Y. Ito as a special case.
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 G. Baxter, A general ergodic theorem with weighted averages, J. Math. Mech. 14 (1965), 277288. MR 30 #4904. MR 0174704 (30:4904)
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 [4]
 R. V. Chacon and D. S. Ornstein, A general ergodic theorem, Illinois J. Math. 4 (1960), 153160. MR 22 #1822. MR 0110954 (22:1822)
 [5]
 L. W. Cohen, On the mean ergodic theorem, Ann. of Math. (2) 41 (1940), 505509. MR 0002027 (1:339b)
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 Y. Ito, Uniform integrability and the pointwise ergodic theorem, Proc. Amer. Math. Soc. 16 (1965), 222227. MR 30 #2121. MR 0171895 (30:2121)
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 R. Sato, On a general ratio ergodic theorem with weighted averages, Proc. Amer. Math. Soc. 35 (1972), 177178. MR 0303317 (46:2455)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197203088201
PII:
S 00029939(1972)03088201
Keywords:
Positive linear contraction,
individual ergodic theorem,
weak sequential compactness
Article copyright:
© Copyright 1972
American Mathematical Society
