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Proceedings of the American Mathematical Society

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On a factorization problem for convergent sequences and on Hankel forms in bounded sequences


Authors: P. P. B. Eggermont and Y. J. Leung
Journal: Proc. Amer. Math. Soc. 96 (1986), 269-274
MSC: Primary 40H05; Secondary 46A45
DOI: https://doi.org/10.1090/S0002-9939-1986-0818457-3
MathSciNet review: 818457
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Abstract: We solve in the negative the following factorization problem of S. Mazur: Can every convergent sequence be written as $ z(n) = {(n + 1)^{ - 1}}\sum\nolimits_{i = 0}^n {x(i)y(n - i),n = 0,1, \ldots } $, with convergent sequences $ x$ and $ y$? This problem also yields the solution of another problem of S. Mazur regarding bounded Hankel forms on the space of all bounded sequences.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0818457-3
Article copyright: © Copyright 1986 American Mathematical Society