On Power-Bounded Operators and the Pointwise Ergodic Property
Moshe Feder · Proceedings of the American Mathematical Society · 1981
We construct a power-bounded isomorphism $T:{L_p} \to {L_p}$, for $1 < p \leqslant 2$, such that $\left [ {{n^{ - 1}}\sum olimits _{i = 0}^{n - 1} {{T^i}f} } \right ](t)$ is not a.e. convergent. ${T^{ - 1}}$ is also power-bounded.