Geodesic
A Katznelson–Tzafriri type theorem for Cesàro bounded operators
Luciano Abadias1
1 Departamento de Matemáticas Instituto Universitario de Matemáticas y Aplicaciones Universidad de Zaragoza 50009 Zaragoza, Spain
Studia Mathematica, Tome 234 (2016) no. 1, pp. 59-82

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We extend the well-known Katznelson–Tzafriri theorem, originally stated for power-bounded operators, to the case of Cesàro bounded operators of any order $\alpha \gt 0.$ For this purpose, we use a functional calculus between a new class of fractional Wiener algebras and the algebra of bounded linear operators, defined for operators with the corresponding Cesàro boundedness. Finally, we apply the main theorem to get ergodicity results for the Cesàro means of bounded operators.
DOI : 10.4064/sm8436-5-2016
Keywords: extend well known katznelson tzafriri theorem originally stated power bounded operators ces bounded operators order alpha purpose functional calculus between class fractional wiener algebras algebra bounded linear operators defined operators corresponding ces boundedness finally apply main theorem get ergodicity results ces means bounded operators

Luciano Abadias 1

1 Departamento de Matemáticas Instituto Universitario de Matemáticas y Aplicaciones Universidad de Zaragoza 50009 Zaragoza, Spain 
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Luciano Abadias. A Katznelson–Tzafriri type theorem for Cesàro bounded operators. Studia Mathematica, Tome 234 (2016) no. 1, pp. 59-82. doi: 10.4064/sm8436-5-2016

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