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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On power-bounded operators and the pointwise ergodic property


Author: Moshe Feder
Journal: Proc. Amer. Math. Soc. 83 (1981), 349-353
MSC: Primary 47A35; Secondary 46E30
DOI: https://doi.org/10.1090/S0002-9939-1981-0624929-2
MathSciNet review: 624929
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Abstract: We construct a power-bounded isomorphism $ T:{L_p} \to {L_p}$, for $ 1 < p \leqslant 2$, such that $ \left[ {{n^{ - 1}}\sum\nolimits_{i = 0}^{n - 1} {{T^i}f} } \right](t)$ is not a.e. convergent. $ {T^{ - 1}}$ is also power-bounded.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0624929-2
Article copyright: © Copyright 1981 American Mathematical Society

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