Sequences of 0's and 1's

Abstract

Abstract. We investigate the extent to which sequence spaces are determined by the sequences of 0's and 1's that they contain.

Sequences of 0's and 1's: sequence spaces with the separable Hahn property

“…Evidently the Hahn property implies the separable Hahn property and the latter implies the matrix Hahn property. It was shown in [1,Theorem 5.3], and [8,Theorem 1.3] that the converse implications fail in general.…”

“…In [3] it was pointed out that the paper [1] by G. Bennett, J. Boos and T. Leiger contains a nontrivial gap in the proof of Theorem 5.2. This theorem is one of the main results of the paper and it was applied three times (cf.…”

“…Introduction. In [1] (see also [5] and [8]) the authors considered three types of Hahn properties. A sequence space E is said to have the Hahn property, the separable Hahn property and the matrix Hahn property if the implication χ(E) ⊂ F ⇒ E ⊂ F holds whenever F is any FK-space, a separable FK-space and a matrix domain c A respectively.…”

“…In [4] a gliding hump argument was applied to show that two other applications (for ℓ ∞ (|λ|) and ℓ ∞ ∩ z α ) of the theorem in [1] are valid.…”

Addendum to: ``Sequences of 0's and 1's'' (Studia Math. 149 (2002), 75–99)

“…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]).…”