Abstract
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.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 47, No. 4, pp. 82–86, 2013
Original Russian Text Copyright © by R. Armario, F. J. García-Pacheco, and F. J. Pérez-Fernández
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Armario, R., García-Pacheco, F.J. & Pérez-Fernández, F.J. On vector-valued Banach limits. Funct Anal Its Appl 47, 315–318 (2013). https://doi.org/10.1007/s10688-013-0038-4
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DOI: https://doi.org/10.1007/s10688-013-0038-4