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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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