Some new subspaces of an FK-space and defferred Cesàro conullity

Abstract

In this paper, we construct new important subspaces D q p S, D q p W , D q p F and D q p B for a locally convex FK-space X containing ϕ, the space of finite sequences. Then, we show that there is a relation among these subspaces. Also, we study deferred Cesàro conullity of one FK-space with respect to another, and we give some important results. Finally, we examine the deferred Cesàro conullity of the absolute summability domain l A , and show that if l A is deferred Cesàro conull, then A cannot be l-replaceable.We recall (see [2,11]) that the f , β-duals of a subset X of w are 2020): primary 46A45, 40A05; secondary 40C05, 40D05.