Mathematical and functional analysis

Divegrent sequences in Banach spaces

S. A. Rudakov^a, T. N. Rudakova<sup>b

a</sup> Chelyabinsk State University
^b South Ural State University, Chelyabinsk

Abstract: 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.