Some Subspaces of an FK Space and Deferred Ces\`{a}ro Conullity

Abstract

In this paper, we construct new important the subspaces $D_{p}^{q}S$, $D_{p}^{q}W$, $D_{p}^{q}F$ and $D_{p}^{q}B$ for a locally convex FK-space $X$ containing $\phi$, the space of finite sequences. Then we show that there is relation among these subspaces. Also, we study deferred Ces\`{a}ro conullity of one FK-space with respect to another, and we give some important results. Finally, we examine the deferred Ces\`{a}ro conullity of the absolute summability domain $l_A$, and show that if $l_A$ is deferred Ces\`{a}ro conull, then $A$ cannot be $l$-replaceable.