Abstract
The main result of this paper is Theorem 1 (in connection with Corollary 1 (e)), which says that the implication*holds for every separable FK-space F, for every FK-space E containing φ and for certain (for example, solid) FK-AB-spaces Y. At this, φ denotes the space of all finite sequences and WE is the set of all elements of E being weakly sectionally convergent.This result was proved by Bennett and Kalton ([1] and [3]) in the special case that E contains all null sequences and that Y is the space m of all bounded sequences or the space of all sequences almost converging to zero.
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