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Positive L<sup>1</sup>operators associated with nonsingular mappings and an example of E. Hille
E. Hille [Hi1] gave an example of an operator in $L^1[0,1]$ satisfying the mean ergodic theorem (MET) and such that $\mathop {\rm sup}_n \| T^n\| =\infty $ (actually, $\| T^n\| \sim n^{{1/4}})$. This was the first example of a non-power bounded mean ergod