Geodesic
A note on the powers of Cesàro bounded operators
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 1091-1100.

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In this note we give a negative answer to Zem�nek's question (1994) of whether it always holds that a Cesàro bounded operator $T$ on a Hilbert space with a single spectrum satisfies $\lim _{n \rightarrow \infty } \|T^{n+1} - T^n\| = 0.$
Classification : 47A35, 47B37, 47B38
Keywords: Volterra operator; stability of operators 
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     title = {A note on the powers of {Ces\`aro} bounded operators},
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Léka, Zoltán. A note on the powers of Cesàro bounded operators. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 1091-1100. http://geodesic.mathdoc.fr/item/CMJ_2010__60_4_a17/