NOTE ON CHOBANYAN-PECHERSKI CONDITION FOR THE SERIES IN BANACH SPACES


Chobanyan-Pecherski condition is a sufficient condition for the affinity of the sum range of a series in a normed space. This condition is automatically fulfilled for the null-sequences in finite dimensional normed spaces. In this paper we describe some classes of null-sequences in an infinite dimensional normed space l_p,1≤p<∞, satisfying the mentioned condition.