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Barrelled spaces and mean ergodicity

Espacios tonelados y ergodicIDad en media

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Abstract

We characterize quasi-reflexive barrelled and complete locally convex Hausdorff spaces with a basis in terms of the properties of this basis. Moreover we prove that a complete, barrelled lcHs with a basis is quasi-reflexive of order one if and only if for every power bounded operator T, either T or T′ is mean ergodic.

Resumen

Se caracterizan los espacios localmente convexos Hausdorff casi-reflexivos, tonelados y completos con base en función de las propiedades de la base. Además se prueba que un espacio localmente convexo Hausdorff completo y tonelado con base es casi-reflexivo de orden 1 si y sólo si para cada operador T de potencias acotadas, T o T′ es ergódico en media.

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  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań ul. Umultowska 87, 61-614, Poznań, Poland

    Krzysztof Piszczek

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  1. Krzysztof Piszczek
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Piszczek, K. Barrelled spaces and mean ergodicity. Rev. R. Acad. Cien. Serie A. Mat. 104, 5–11 (2010). https://doi.org/10.5052/RACSAM.2010.02

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  • DOI: https://doi.org/10.5052/RACSAM.2010.02

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