Dual pairs of sequence spaces.
There is a nontrivial gap in the proof of Theorem 5.2 of [2] which is one of the main results of that paper and has been applied three times (cf. [2, Theorem 5.3, (G) in Section 6, Theorem 6.4]). Till now neither the gap has been closed nor a counterexample found. The aim of this paper is to give, by means of some general results, a better understanding of the gap. The proofs that the applications hold will be given elsewhere.
We investigate the extent to which sequence spaces are determined by the sequences of 0's and 1's that they contain.
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