Geodesic
Divegrent sequences in Banach spaces
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 10 (2008), pp. 5-18

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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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     author = {S. A. Rudakov and T. N. Rudakova},
     title = {Divegrent sequences in {Banach} spaces},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {5--18},
     publisher = {mathdoc},
     number = {10},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2008_10_a0/}
}
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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/