Summation of almost convergent divergent sequences,topological methods

In this paper we give a characterization of the conservative matrices that sum only those divergent sequences which are not almost convergent. Such conditions are similar to those which are necessary and sufficient for a conservative matrix to sum no bounded divergent sequence (Agnew 1], Mazur-Orlicz 4], Wilansky-Zeller 6], and Zeller 7]). There are, however, some differences showing, that the results mentioned above cannot be transmitted without any restriction. Parts of this paper have been already developed by the author more detailed in 5].