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

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Mugnolo D.

Studia Mathematica

2004

tom 164

nr 3

243-251

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.

Ograniczanie wyników

1 Studia Mathematica

1 Mugnolo D.

1 2004

Wyniki wyszukiwania

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