A semigroup analogue of the Fonf–Lin–Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis

Volume 164 / 2004

Delio Mugnolo Studia Mathematica 164 (2004), 243-251 MSC: Primary 47A35. DOI: 10.4064/sm164-3-3


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.


  • Delio MugnoloArbeitsbereich Funktionalanalysis
    Mathematisches Institut
    der Universität Tübingen
    Auf der Morgenstelle 10
    D-72076 Tübingen, Germany
    Dipartimento di Matematica
    Università degli Studi di Bari
    Via E. Orabona 4
    I-70125 Bari, Italy

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