Abstract
In this paper we study the almost convergence and the almost summability in normed spaces. Among other things, spaces of sequences defined by the almost convergence and the almost summability are proved to be complete if the basis normed space is so. Finally, some classical properties such as completeness, reflexivity, Schur property, Grothendieck property, and the property of containing a copy of c 0 are characterized in terms of the almost convergence.
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Acknowledgements
This paper is supported by project MTM2006-15546-C02-01 “Álgebras de Banach y espacios de Banach” (Ministry of Science and Education, Spain) and by the Research Group FQM-257 “Geometry, Operators, and Series in Banach Spaces” (Autonomous Government of Andalusia).
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∗ Since deceased.
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AIZPURU, A., ARMARIO*, R., GARCÍA-PACHECO, F.J. et al. Vector-valued almost convergence and classical properties in normed spaces. Proc Math Sci 124, 93–108 (2014). https://doi.org/10.1007/s12044-013-0160-5
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DOI: https://doi.org/10.1007/s12044-013-0160-5