Geodesic
A Katznelson–Tzafriri type theorem for Cesàro bounded operators
Luciano Abadias1
1Departamento 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 
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
@article{10_4064_sm8436_5_2016,
     author = {Luciano Abadias},
     title = {A {Katznelson{\textendash}Tzafriri} type theorem for {Ces\`aro} bounded operators},
     journal = {Studia Mathematica},
     pages = {59--82},
     year = {2016},
     volume = {234},
     number = {1},
     doi = {10.4064/sm8436-5-2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm8436-5-2016/}
}
TY  - JOUR
AU  - Luciano Abadias
TI  - A Katznelson–Tzafriri type theorem for Cesàro bounded operators
JO  - Studia Mathematica
PY  - 2016
SP  - 59
EP  - 82
VL  - 234
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm8436-5-2016/
DO  - 10.4064/sm8436-5-2016
LA  - en
ID  - 10_4064_sm8436_5_2016
ER  - 
%0 Journal Article
%A Luciano Abadias
%T A Katznelson–Tzafriri type theorem for Cesàro bounded operators
%J Studia Mathematica
%D 2016
%P 59-82
%V 234
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm8436-5-2016/
%R 10.4064/sm8436-5-2016
%G en
%F 10_4064_sm8436_5_2016

Cité par Sources :