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arXiv · 2512.01397

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

Delio Mugnolo
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Abstract

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.

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Delio Mugnolo. 2025-12-01. A semigroup analogue of the Fonf--Lin--Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis. https://doi.org/10.4064/sm164-3-3

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