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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On power-bounded operators and the pointwise ergodic property
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by Moshe Feder PDF
Proc. Amer. Math. Soc. 83 (1981), 349-353 Request permission

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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Additional Information
  • © Copyright 1981 American Mathematical Society
  • 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