Geodesic
The Unrestricted Section Properties of Sequences
Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 331-336

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction. An unrestricted section of a sequence x is any sequence of the form Σk∈F x k δk , where F is some finite subset of the natural numbers. The notion of boundedness of the set of unrestricted sections of a sequence in a K-space was studied in [10], and called unconditional section boundedness (UAB). It was shown in [10] (Theorem 7) that the class of FK-spaces in which every element has UAB consists of those FK-spaces that are invariant under coordinatewise multiplication by the convergent sequences. 
Sember, John; Raphael, Marc. The Unrestricted Section Properties of Sequences. Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 331-336. doi: 10.4153/CJM-1979-036-1
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[1] 1. Buntinas, M., Convergent and bounded Cesàro sections in FK-spaces, Math. Z. 121 (1971), 191–200. Google Scholar

[2] 2. Buntinas, M., On Toeplitz sections in sequence spaces, Proc. Cambridge Philos. Soc. 78 (1975), 451–460. Google Scholar

[3] 3. Day, M. M., Normed linear spaces.(Berlin-Gôttingen-Heidelberg, 1962). Google Scholar

[4] 4. Garling, D. J. H., On topological sequence spaces, Proc. Cambridge Philos. Soc. 63 (1967), 997–1019. Google Scholar

[5] 5. Goes, G., Summen von FK-raumen, funktionale abschnittskonvergenz una Umkehrsatze, Tôhoku Math. J. 26 (1974), 487–504. Google Scholar

[6] 6. Goffman, C. and Pedrick, G., First course in functional analysis (Englewood Cliffs, N.J., 1965). Google Scholar

[7] 7. McArthur, C. W., On a theorem of Orlicz and Pettis, Pacific J. Math. 22 (1967), 297–302. Google Scholar

[8] 8. Robertson, A. P., On unconditional convergence in topological vector spaces, Proc. Roy. Soc. Edin., Sect. A 68 (II) (1969), 145–157. Google Scholar

[9] 9. Robertson, A. P. and Robertson, W. J., Topological vector spaces (Cambridge, 1964). Google Scholar

[10] 10. Sember, J. J., On unconditional section boundedness in sequence spaces, Rocky Mountain J. of Math. Vol. 7, No. 4, (1977). Google Scholar

[11] 11. Snyder, A. K., Conull and coregular FK-spaces, Math Z. 90, (1965), 376–381. Google Scholar

[12] 12. Wilansky, A., Functional analysis (New York, 1964). Google Scholar

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