Abstract
As pointed out in [4] the paper [2], authored by G. Bennett, J. Boos and T. Leiger, contains a nontrivial gap in the argumentation of the proof of Theorem 5.2 which is one of main results of that paper and has been applied three times. Till now neither the gap is closed nor a counterexample has been stated. That is why the authors have examined in [4] the situation around the ‘gap’ aiming to a better understanding for the gap. The aim of this paper is to prove the mentioned applications of the theorem in doubt by using gliding hump arguments (quite similar to the classical proofs of the Theorems of Schur and Hahn in the first case (cf. [3]) and a very technical and artful construction, being of independent mathematical interest, in the second case).
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Dedicated to the memory of Karl Zeller
Research of T. Leiger supported by Estonian Science Foundation Grant 5376.
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Boos, J., Leiger, T. Sequences of 0’s and 1’s: Special sequence spaces with the separable Hahn property. Acta Math Hung 115, 341–356 (2007). https://doi.org/10.1007/s10474-007-5278-4
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DOI: https://doi.org/10.1007/s10474-007-5278-4
Key words and phrases
- Hahn property
- Nikodym property
- separable Hahn property
- matrix Hahn property
- inclusion theorems
- dense barrelled subspaces
- Hahn theorem