Geodesic
Divegrent sequences in Banach spaces
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 10 (2008), pp. 5-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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The method of construction of the class of the sequences not containing pseudo-converging subsequences (summable by arithmetic means) is developed. The example of a Banach space of sequences with some topology is constructed that containing pseudo-converging, divergent in the sence of norm sequences, but all not containing pseudo-converging subsequences sequences diverges. 
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S. A. Rudakov; T. N. Rudakova. Divegrent sequences in Banach spaces. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 10 (2008), pp. 5-18. http://geodesic.mathdoc.fr/item/VCHGU_2008_10_a0/

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