# 20 novembre 2018: 1 événement

### Mardi 20 novembre 2018 13:45-14:45 - Waed Dada - Université Wuppertal

Cesàro bounded operators on Banach spaces

Résumé : In the first part of my talk I will explain the paper [1]. The authors gave several notations of boundedness for operators like strongly Kreiss bounded, uniformly Kreiss bounded and Kreiss bounded operators. It is known that any power bounded operator is absolutely Cesaro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general.
Moreover, they obtained also a characterization of power boundeded operators which generalizes a results in [2].
Aleman and Suciu in [3] asked if every uniformly Kreiss bounded operator $T$ on a Banach space satisfies that $\lim \|T^n/n\|=0$. The authors in [1] solve this question for operators on Hilbert spaces. In addition, they proved that, if $T$ is absolutely Cesaro bounded on a Banach (Hilbert) space, then $\|T^n\|=o(n)$.
As a consequence, every absolutely Cesaro bounded operator on a reflexive Banach space is mean ergodic.
In the second part of my talk I will answer the question : ”Are the Tadmor-Ritt operators mean ergodic ?” for simple cases for operators.
References
[1] Bemudez T., Bonilla A., Muller V. and Peris A., Cesaro bounded operators in Banach spaces, preprint (2018).
[2] Van Casteren J. A., Boundedness properties of resolvents and semigroups of operators. Linear operators Banach Center Publ., 38, Polish Acad. Sci. Inst. Math., Warsaw, (1997) 59–74.
[3] Aleman A. and Suciu L., On ergodic operator means in Banach spaces, Integral Equations Operator Theory, 85 (2016) 259–287.

Lieu : 316Bbis

En savoir plus : Séminaire d’Analyse Fonctionnelle