We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesàro bounded and strong Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing absolutely Cesàro bounded operators on ℓ p (N), 1 ≤ p < ∞, which are not power bounded, and provide examples of uniformly Kreiss bounded operators which are not absolutely Cesàro bounded. These results complement very limite…
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