Geodesic
On Vector-Valued Banach Limits
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 4, pp. 82-86

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In this brief communication we propose a vector-valued version of Lorentz' intrinsic characterization of almost convergence, for which we find a legitimate extension of the concept of Banach limit to vector-valued sequences. Banach spaces $1$-complemented in their biduals admit vector-valued Banach limits, whereas $c_0$ does not.
Keywords: Banach limit, almost convergence. 
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R. Armario; F. J. Garcia-Pacheco; F. J. Perez-Fernandez. On Vector-Valued Banach Limits. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 4, pp. 82-86. http://geodesic.mathdoc.fr/item/FAA_2013_47_4_a6/