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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The gliding humps technique for $ FK$-spaces


Author: G. Bennett
Journal: Trans. Amer. Math. Soc. 166 (1972), 285-292
MSC: Primary 40H05
MathSciNet review: 0296564
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Abstract: The gliging humps technique has been used by various authors to establish the existence of bounded divergent sequences in certain summability domains. The purpose of this paper is to extend these results and to obtain analogous ones for sequence spaces other than c and m. This serves to unify and improve many known results and to obtain several new ones--applications include extensions to theorems of Dawson, Lorentz-Zeller, Snyder-Wilansky and Yurimyae. Improving another result of Wilansky allows us to consider countable collections of sequence spaces--applications including the proof of a conjecture of Hill and Sledd and extensions to theorems of Berg and Brudno. A related result of Petersen is also considered and a simple proof using the Baire category theorem is given.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0296564-9
PII: S 0002-9947(1972)0296564-9
Keywords: Gliding humps technique, Baire category theorem, FK-space, matrix transformation, countable collections of matrices, (bounded) convergence domain, absolute summability domain, ultimately almost periodic sequences, almost convergent sequences
Article copyright: © Copyright 1972 American Mathematical Society