Geodesic
A semigroup analogue of the Fonf–Lin–Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis
Delio Mugnolo1
1 Arbeitsbereich Funktionalanalysis Mathematisches Institut der Universität Tübingen Auf der Morgenstelle 10 D-72076 Tübingen, Germany and Dipartimento di Matematica Università degli Studi di Bari Via E. Orabona 4 I-70125 Bari, Italy
Studia Mathematica, Tome 164 (2004) no. 3, pp. 243-251

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

In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space $X$ with a basis. (i) $X$ is finite-dimensional if and only if every bounded, uniformly continuous, mean ergodic semigroup on $X$ is uniformly mean ergodic. (ii) $X$ is reflexive if and only if every bounded strongly continuous semigroup is mean ergodic if and only if every bounded uniformly continuous semigroup on $X$ is mean ergodic.
DOI : 10.4064/sm164-3-3
Keywords: analogy recent result fonf lin wojtaszczyk prove following characterizations banach space basis finite dimensional only every bounded uniformly continuous mean ergodic semigroup uniformly mean ergodic reflexive only every bounded strongly continuous semigroup mean ergodic only every bounded uniformly continuous semigroup mean ergodic

Delio Mugnolo 1

1 Arbeitsbereich Funktionalanalysis Mathematisches Institut der Universität Tübingen Auf der Morgenstelle 10 D-72076 Tübingen, Germany and Dipartimento di Matematica Università degli Studi di Bari Via E. Orabona 4 I-70125 Bari, Italy 
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Delio Mugnolo. A semigroup analogue of the
  Fonf–Lin–Wojtaszczyk ergodic characterization of
  reflexive Banach spaces with a basis. Studia Mathematica, Tome 164 (2004) no. 3, pp. 243-251. doi: 10.4064/sm164-3-3

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