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A resolvent condition implying power boundedness

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The Ritt and Kreiss resolvent conditions are related to the behaviour of the powers and their various means. In particular, it is shown that the Ritt condition implies the power boundedness. This improves the Nevanlinna characterization of the sublinear decay of the differences of the consecutive powers in the Esterle-Katznelson-Tzafriri theorem, and actually characterizes the analytic Ritt condition by two geometric properties of the powers.
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  • Mathematical Institute, Technical University of Budapest, Egry József u. 2, H. ép., II. em., H-1521 Budapest XI, Hungary
  • Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, 00-950 Warszawa, Poland
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