On a factorization problem for convergent sequences and on Hankel forms in bounded sequences
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- by P. P. B. Eggermont and Y. J. Leung
- Proc. Amer. Math. Soc. 96 (1986), 269-274
- DOI: https://doi.org/10.1090/S0002-9939-1986-0818457-3
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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.References
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- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- 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