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Sequences of 0’s and 1’s. (English) Zbl 0995.46010

Stud. Math. 149, No. 1, 75-99 (2002); addendum ibid. 171, No. 3, 305-309 (2005).
In this paper the authors investigate the problem to what extend a given sequence space may be determined by the linear span of the sequences of 0s and 1s contained in the space. They have done here an extensive study of this problem and several theorems are given. They also give several concrete illustrations of the results discussed in the paper. Further they have a list of problems, some of which are still open, while for some others they suggest what level of finalization is achievable presently.

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
46A35 Summability and bases in topological vector spaces
40C05 Matrix methods for summability
40H05 Functional analytic methods in summability
46A08 Barrelled spaces, bornological spaces
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